Digital Photogrammetry - TEC-Digital

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Digital Photogrammetry
Architectural photogrammetry i
Photogrammetry, the use of photography for surveying, primarily facilitates the
production of maps and geographic databases from aerial photographs. Along with
remote sensing, it represents the principal means of generating data for geographic
information systems.
Photogrammetry has undergone a remarkable evolution in recent years with its
transformation into ‘digital photogrammetry’. First, the distinctions between
photogrammetry, remote sensing, geodesy and GIS are fast disappearing, as data
can now be carried digitally from the plane to the GIS end-user. And second, the
benefits of digital photogrammetric workstations have increased dramatically. The
comprehensive use of digital tools, and the automation of the processes, have significantly
cut costs and reduced processing time. The first digital aerial cameras have
become available, and the introduction of more and more new digital tools allows
the work of operators to be simplified, without the same need for stereoscopic
skills. Engineers and technicians in other fields are now able to carry out photogrammetric
work without reliance on specialist photogrammetrists.
This book shows non-experts what digital photogrammetry is and what the software
does, and provides them with sufficient expertise to use it. It also gives
specialists an overview of these totally digital processes from A to Z. It serves as
a textbook for graduate students, young engineers and university lecturers to
complement a modern lecture course on photogrammetry.
Michel Kasser and Yves Egels have synthesized the contributions of 21 topranking
specialists in digital photogrammetry, lecturers, researchers, and production
engineers, and produced a very up-to-date text and guide.
Michel Kasser, who graduated from the École Polytechnique de Paris and from
the École Nationale des Sciences Géographiques (ENSG), was formerly Head of
ESGT, the main technical university for surveyors in France. A specialist in instrumentation
and space imagery, he is now University Professor and Head of the
Geodetic Department at IGN-France.
Yves Egels, who graduated from the École Polytechnique de Paris and from ENSG,
is senior photogrammetrist at IGN-France, where he pioneered analytical plotter
software in the 1980s and digital workstations on PCs in the 1990s. He is now
Head of the Photogrammetric Department at ENSG and lectures in photogrammetry
at various French technical universities.

ii Pierre Grussenmeyer, Klaus Hanke, André Streilein

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Digital Photogrammetry
Michel Kasser and Yves Egels
London and New York
Architectural photogrammetry iii

First published 2002
by Taylor & Francis
11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada
by Taylor & Francis Inc,
29 West 35th Street, New York, NY 10001
Taylor & Francis is an imprint of the Taylor & Francis Group
This edition published in the Taylor & Francis e-Library, 2004.
© 2002 Michel Kasser and Yves Egels
All rights reserved. No part of this book may be reprinted or
reproduced or utilised in any form or by any electronic, mechanical,
or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or
retrieval system, without permission in writing from the publishers.
Every effort has been made to ensure that the advice and
information in this book is true and accurate at the time of going to
press. However, neither the publisher nor the authors can accept
any legal responsibility or liability for any errors or omissions that
may be made. In the case of drug administration, any medical
procedure or the use of technical equipment mentioned within this
book, you are strongly advised to consult the manufacturer’s
guidelines.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the
British Library
Library of Congress Cataloging in Publication Data
Kasser, Michel
Digital photogrammetry/Michel Kasser and Yves Egels.
p. cm
Includes bibliographical references and index.
I. Aerial photogrammetry. 2. Image processing – Digital techniques.
I. Kasser, Michel. II. Title.
TA 593.E34 2001
526.9′82 – dc21 2001027205
ISBN 0-203-30595-7 Master e-book ISBN
ISBN 0-203-34383-2 (Adobe eReader Format)
ISBN 0–748–40945–9 (pbk)
ISBN 0–748–40944–0 (hbk)

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Contents
List of colour plates viii
List of contributors ix
Introduction xiii
1 Image acquisition. Physical aspects. Instruments 1
Introduction 1
1.1 Mathematical model of the geometry of the aerial
image 2
YVES EGELS
1.2 Radiometric effects of the atmosphere and the optics 16
MICHEL KASSER
1.3 Colorimetry 25
YANNICK BERGIA, MICHEL KASSER
1.4 Geometry of aerial and spatial pictures 34
MICHEL KASSER
1.5 Digital image acquisition with airborne CCD cameras 39
MICHEL KASSER
1.6 Radar images in photogrammetry 47
LAURENT POLIDORI
1.7 Use of airborne laser ranging systems for the
determination of DSM 53
MICHEL KASSER
1.8 Use of scanners for the digitization of aerial pictures 58
MICHEL KASSER
1.9 Relations between radiometric and geometric precision
in digital imagery 63
CHRISTIAN THOM
Architectural photogrammetry v

vi Contents
2 Techniques for plotting digital images 78
Introduction 78
2.1 Image improvements 79
ALAIN DUPÉRET
2.2 Compression of digital images 100
GILLES MOURY
2.3 Use of GPS in photogrammetry 115
THIERRY DUQUESNOY, YVES EGELS, MICHEL KASSER
2.4 Automatization of aerotriangulation 124
FRANCK JUNG, FRANK FUCHS, DIDIER BOLDO
2.5 Digital photogrammetric workstations 145
RAPHAËLE HENO, YVES EGELS
3 Generation of digital terrain and surface models 159
Introduction 159
3.1 Overview of digital surface models 159
NICOLAS PAPARODITIS, LAURENT POLIDORI
3.2 DSM quality: internal and external validation 164
LAURENT POLIDORI
3.3 3D data acquisition from visible images 168
NICOLAS PAPARODITIS, OLIVIER DISSARD
3.4 From the digital surface model (DSM) to the digital
terrain model (DTM) 221
OLIVIER JAMET
3.5 DSM reconstruction 225
GRÉGOIRE MAILLET, PATRICK JULIEN,
NICOLAS PAPARODITIS
3.6 Extraction of characteristic lines of the relief 253
ALAIN DUPÉRET, OLIVIER JAMET
3.7 From the aerial image to orthophotography: different
levels of rectification 282
MICHEL KASSER, LAURENT POLIDORI
3.8 Production of digital orthophotographies 288
DIDIER BOLDO
3.9 Problems relating to orthophotography production
DIDIER MOISSET 292

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4 Metrologic applications of digital photogrammetry 300
Introduction 300
4.1 Architectural photogrammetry 300
PIERRE GRUSSENMEYER, KLAUS HANKE,
ANDRÉ STREILEIN
4.2 Photogrammetric metrology 340
MICHEL KASSER
Contents vii
Index 349

viii Pierre Grussenmeyer, Klaus Hanke, André Streilein
Plates
There is a colour plate section between pages 192 and 193
Figure 3.3.20 Left and right images of a 1m ground pixel size satellite
across track stereopair; DSM result with a classical crosscorrelation
technique; DSM using adaptive shape windows
Figure 3.3.24 An example of the management of hidden parts
Figure 3.3.27 Correlation matrix corresponding to the matching of the
two epipolar lines appearing in yellow in the image extracts
Figure 3.3.28 Results of the global matching strategy on a complete
stereopair overlap in a dense urban area
Figure 3.4.1 Images from the digital camera of IGN-F (1997) on Le
Mans (France)
Figure 3.8.3 Scanned images before balancing
Figure 3.8.4 Scanned images after balancing
Figure 3.9.2 Example from a real production problem: the radiometric
balancing on digitized pictures
Figure 3.9.4 Examples from the Ariège, France: problems posed by cliffs
Figure 3.9.5 Generation of stretched pixels
Figure 3.9.6 Example of radiometric difficulties (Ariège, France)
Figure 3.9.7 Example of typical problems on water surfaces
Figure 3.9.8 Two examples from the Isère department, France
Figure 3.9.9 Two examples, using the digital aerial camera of IGN-F

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Contributors
Architectural photogrammetry ix
Yannick Bergia, born in 1977, graduated as an informatics engineer from
ISIMA (Institut Supérieur d’Informatique, de Modélisation et de leurs
Applications, Clermont-Ferrand, France) in 1999. He performed his
diploma work in MATIS in 1999, and is a specialist in image processing.
y.bergia@infonie.fr
Didier Boldo, born in 1973, graduated from the École Polytechnique de
Paris and from ENSG. He is now pursuing a Ph.D. in pattern recognition
and image analysis at MATIS. His main research interests are
photogrammetry, 3D reconstruction and radiometric modelling and calibration.
didier.boldo@ign.fr
Olivier Dissard, born in 1967, graduated from the École Polytechnique de
Paris and from ENSG. Previously in charge of research concerning 3D
urban topics at MATIS laboratory, he is now in charge of digital
orthophotography at IGN-F. His studies at MATIS have concerned
urban DEM and DSM, focusing on raised structures and classification
in buildings and vegetation, and true orthophotographies.
olivier.dissard@ign.fr
Alain Dupéret graduated as ingénieur géographe from ENSG. He started
working as a surveyor in IGN-F in 1979 and undertook topographic
missions in France and Africa before specialising in image processing
and DTM production. After managing technical projects and giving
lectures in photogrammetry and image processing in ENSG, he became
Head of Studies Management at ENSG.
duperet@ensg.ign.fr
Thierry Duquesnoy (born in 1963) graduated from ENSG in 1989. He
gained his Ph.D. in earth sciences in 1997 at the University of Paris.
He has worked since 1989 with the LOEMI, where he is a specialist in
GPS trajectography for photogrammetry.
thierry.duquesnoy@ign.fr

x Contributors
Yves Egels, born in 1947, graduated from the École Polytechnique de Paris
and from ENSG, and is senior photogrammetrist at IGN-F, where he
pioneered analytical plotter software in the 1980s and digital workstations
on PCs in the 1990s. He is now Head of the Photogrammetric
Department at ENSG and gives lectures in photogrammetry at various
French technical universities.
egels@ensg.ign.fr
Frank Fuchs, born in 1971, graduated from the École Polytechnique de
Paris and from ENSG. Since 1996 he has been working at MATIS on
his Ph.D. concerning the automatic reconstruction of buildings in aerial
imagery through a structural approach.
frank.fuchs@ign.fr
Pierre Grussenmeyer, born in 1961, graduated from ENSAIS, and gained a
Ph.D. in photogrammetry in 1994 at the University of Strasbourg in
collaboration with IGN-F. He has been on the academic staff of the
Department of Surveying at ENSAIS, where he teaches photogrammetry,
since 1989. Since 1996 he has been Professor and the Head of the
Photogrammetry and Geomatics Group at ENSAIS-LERGEC.
pierre.grussenmeyer@ensais.u-strasbg.fr
Klaus Hanke, born 1954, studied geodesy and photogrammetry at the
University of Innsbruck and the Technical University of Graz. In 1984
he became Dr. techn., and since 1994 he has been a Professor teaching
Photogrammetry and Architectural Photogrammetry at the University
of Innsbruck.
Raphaële Heno, born 1970, graduated in 1993 from ENSG and from ITC
(Enschede – The Netherlands). She spent four years developing digital
photogrammetric tools to improve IGN-France topographic database
plotting. Since 1998 she has been senior consultant for the IGN-France
advisory department.
raphaele_heno@hotmail.com
Olivier Jamet, born in 1963, graduated from the École Polytechnique de
Paris and from ENSG. He gained a Ph.D. in signal and image processing
at the École Nationale Supérieure des Télécommunications de Paris
(1998). Formerly Head of the MATIS laboratory, he is currently in
charge of research in physical geodesy at LAREG, ENSG.
olivier.jamet@ign.fr
Patrick Julien graduated from the University of Paris (in mathematics) and
from ENSG, and joined IGN-F in 1975. He has developed various softwares
for orthophotography, digital terrain models and digital image
matching. He is presently a researcher at MATIS and gives lectures at
ENSG in geographic information sciences.
patrick.julien@ign.fr

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Contributors xi
Franck Jung, born in 1970, graduated from the École Polytechnique de
Paris and from ENSG, and is currently a researcher at the MATIS laboratory.
He is preparing a Ph.D. dissertation on automatic change
detection using aerial stereo pairs at two different dates. His main
research interests are automatic digital photogrammetry, change detection
and machine learning.
franck.jung@ign.fr
Michel Kasser, born in 1953, graduated from the École Polytechnique de
Paris and from ENSG. He created the LOEMI in 1984 and was from
1991 to 1999 head of the ESGT. As a specialist in instrumentation, in
geodesy and in space imagery, he is University Professor and Head of
the Geodetic Department and of LAREG at IGN-F.
michel.kasser@ign.fr
Grégoire Maillet, born in 1973, graduated from ENSG in 1997. He is now
a research engineer at MATIS, where he works on dynamic programming
and automatic correlation for image matching.
gregoire.maillet@ign.fr
Didier Moisset, born in 1958, obtained the ENSG engineering degree in
1983. He was in charge of the aerotriangulation team at IGN in 1989,
and was Professor in photogrammetry and Head of the Photogrammetric
Department at the ENSG during 1993–8. He was a project manager in
1998 and developed new automatic orthophoto software for IGN. He
was recently appointed as a consultant in photogrammetry at the MATIS
laboratory.
didier.moisset@ign.fr
Gilles Moury, born in 1960, graduated from the École Polytechnique de
Paris and from ENSAE (École Nationale Supérieure de l’Aéronautique
et de l’Espace). He has been working in the field of satellite on-board
data processing since 1985, within CNES. In particular, he was responsible
for the development of image compression algorithms for various
space missions (Spot 5, Clementine, etc.). He is now Head of the onboard
data processing section and lectures in data compression at various
French technical universities.
gilles.moury@cnes.fr
Nicolas Paparoditis, born in 1969, obtained a Ph.D. in computer vision
from the University of Nice-Sophia Antipolis. He worked for five years
for the Aérospatiale Company on the specification of HRV digital
mapping satellite instruments (SPOT satellites). He is a specialist in
image processing, in computer vision, and in digital aerial and satellite
imagery, and is currently a Professor at ESGT where he leads the research
activities in digital photogrammetry. He is also a research member of
MATIS at IGN-F.
nicolas.paparoditis@ign.fr

xii Contributors
Laurent Polidori, born in 1965, graduated from ENSG in 1987. He gained
a Ph.D. in 1991 on ‘DTM quality assessment for earth sciences’ at Paris
University. A researcher at the Aérospatiale Company (Cannes, France)
on satellite imagery, he is the author of Cartographie Radar (Gordon
and Breach, 1997). He is Head of the Remote Sensing Laboratory of
IRD (Cayenne, Guyane) and Associate Professor at ESGT.
polidori@caiena.cayenne.ird.fr
André Streilein in 1990 obtained a Dip.Ing. at the Rheinische Friedrich-
Wilhelms-Universität, Bonn. In 1998 he obtained a Dr. sc. tech. at the
Swiss Federal Institute of Technology, Zurich. His dissertation was on
‘Digitale Photogrammetrie und CAAD’. Since September 2000 he has
been at the Swiss Federal Office of Topography (Bern), Section
Photogrammetry and Remote Sensing. (Postal address: Bundesamt für
Landestopographie, Seftigenstrasse 2, 3084 Wabern, Bern, Switzerland.)
Christian Thom, born in 1959, graduated from the École Polytechnique
de Paris and from the ENSG. With a Ph.D. (1986) in robotics and signal
processing, he has specialized in instrumentation. He is Head of LOEMI
where he pioneered and developed the IGN program of digital aerial
cameras from 1989.
christian.thom@ign.fr
Institutions
IGN-F is the Institut Géographique National, France, administration in
charge of national geodesy, cartography and geographic databases. Its main
installation is in Saint-Mandé, close to Paris. The MATIS is the laboratory
for research in photogrammetry of IGN-F; the LOEMI is its laboratory
for new instrument development; and the LAREG its laboratory for
geodesy. The ENSG (École Nationale des Sciences Géographiques) is the
technical university owned by IGN-F.
(Postal address: IGN, 2 Avenue Pasteur, F-94 165 Saint-Mandé Cedex,
France.)
The CNES is the French Space Agency.
(Postal address: CNES, 2 Place Maurice Quentin, F-75 039 Paris Cedex
01, France.)
The ENSAIS is a technical university in Strasbourg with a section of engineers
in surveying.
(Postal address: ENSAIS, 24 Boulevard de la Victoire, F-67 000, Strasbourg,
France.)
The ESGT is the École Supérieure des Géomètres et Topographes
(Le Mans), the technical university with the most important section of
engineers in surveying in France.
(Postal address: ESGT, 1 Boulevard Pythagore, F-72 000, Le Mans, France.)

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Introduction
Architectural photogrammetry xiii
In 1998, when Taylor & Francis pushed me into the adventure of writing
this book with my colleague Yves Egels, most specialists of photogrammetry
around me were aware of the lack of communication between their
technical community and other specialists. Indeed, this situation was not
new, as 150 years after its invention by Laussédat photogrammetry was
really reserved for photogrammetrists (considering for example the
extremely high costs of photogrammetric plotters, but also the necessary
visual ability of the required technicians, a skill that required a long and
costly training, etc.). Photogrammetry was thus the speciality of a very
small club, mostly European, and the related industrial activity was heavily
based on the national cartographic institutions.
As we saw it in the early 1990s, the situation has changed very rapidly
with the improvement of the computational power available on cheap
machines. First, one could see software developments trying to avoid the
mechanical part of the photogrammetric plotters, but more or less based
on the same algorithms as analytical plotters. These machines, still devoted
to professional practitioners, appeared a little cheaper, but with a comparatively
poor visual quality. They were often considered as good workstations
for orthophotographic productions with, as a side quality, an additional
production capacity of photogrammetric plotting in case of emergency
work. The main residual difficulty was linked to the huge amount of bytes,
and also to the digitization of the traditional argentic aerial images, as the
necessary scanners were extremely expensive. The high cost of the very precise
mechanical parts had already been reduced in the 1980s from the old
opto-mechanical plotters to the analytical plotters, as the mechanics has
been downsized from 3D to 2D. But as a final revolution they had just
shifted from the analytical plotter to the scanner, although a scanner could
be used for many plotting workstations, and thus the total production cost
was already lower. But this necessity to use a high-cost scanner was the
main limitation of any new development of photogrammetric activity.
During this period, the industry developed for the consumer public very
interesting products devoted to following the explosion of the microinformatics
evolution and providing a set of extremely cheap tools: video

xiv Introduction
cards allowing a fast and nearly real-time image management, stereoscopic
glasses for video games, A4 scanners, digital colour cameras, etc. These
developments were quickly taken into account by photogrammetrists, so
that the Digital Photogrammetric Workstations (DPW) became cheaper
and cheaper, most of the cost today being the software cost. This has
completely changed the situation of photogrammetry: it is now possible
to own a DPW and to use it only occasionally, as the acquisition costs
are low. And if the user lacks a good stereoscopic vision capability, the
automatic matching will help him to put the floating point in good contact
with the surveyed zone. Of course, only trained people may quickly survey
a large amount of data in a cost-effective way, but a good possibility to
work is opened to non-specialists.
If the situation changed a lot for non-photogrammetrists, in fact it
changed a lot for the photogrammetrists themselves, too: the main revolution
we have met in the 1990s is the availability of aerial digital cameras,
providing images whose quality is far superior to the classic argentic ones,
at least in terms of radiometric fidelity, noise level, and geometric perfection.
Thus the last obstacle for a wide spreading of digital photogrammetry
is disappearing. We are on the verge of a massive transfer of such techniques
toward purely digital processes, and the improvement in quality of
the products, hopefully, should be very significant in the next few years.
Also, the use of digital images allows us to automate more and more tasks,
even if a large part of the automation is still at a research level (most automatic
cue extractions).
We have then a completely new situation, where (for a basic activity at
least) the equipment is no longer a limit for a wide spread of photogrammetric
methodology. But if the use is now spreading rapidly, the theoretical
aspects are not sufficiently known today, which could result in disappointing
results for newcomers.
Thus this book has been oriented towards engineers and technicians,
including technicians who are basically external to the field of photogrammetry
and who would like to understand at least part of this field, for
example to use it from time to time, without the help of professionals of
photogrammetry. The goal here is to get this specialty much closer to the
end user, and to help him to be autonomous in most circumstances, a little
like word processors allowed us to type what we wanted when we wanted
it, twenty years ago. But this end user must already have a scientific and
technical culture, as the theoretical concepts would not be accessible
without such a background. So I have supposed in this publication that
the reader had such an initial understanding. Of course, professors and
students, young ones as well as former specialists going through Continuous
Professional Development, will also find great benefit from this up-to-date
material.
A final very important point: the goal here being to be extremely close
to the practical applications and to the production of data, we have looked

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Introduction xv
for co-authors who are, each of them, excellent specialists in given aspects
of digital photogrammetry, and most of them are practitioners or directly
working for them. This is a guarantee that the considerations discussed
here are really close to the application world. But the unavoidable drawback
is that we have here 21 different authors for a single book, and that
despite our efforts it is obvious that the homogeneity is not perfect. Some
aspects are presented twice, sometimes with significant differences of point
of view: this will remind each of us that the reality is complex, even in
technical matters, and that controversy is the essence of our societies. In
any case we have included an abundant bibliography that may be useful
for further reading. Of course, as many authors are from France, most of
the illustrations come from studies performed in this country, especially
as IGN-F has been one of the few pioneers of the digital CCD cameras.
But I think that this material is more or less equivalent to what everybody
may find in his own country, especially now that large companies commercially
propose digital cameras.
Michel Kasser

xvi Pierre Grussenmeyer, Klaus Hanke, André Streilein

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1 Image acquisition. Physical
aspects. Instruments
INTRODUCTION
We may define photogrammetry as ‘any measuring technique allowing the
modelling of a 3D space using 2D images’. Of course, this is perfectly suitable
for the case where one uses photographic pictures, but this is still the
case when any other type of 2D acquisition device is used, for example a
radar, or a scanning device: the photogrammetric process is basically independent
of the image type. For that reason, we will present in this chapter
the general physical aspects of the data acquisition in digital photogrammetry.
It starts with §1.1, a presentation of the geometric aspects of
photogrammetry, which is a classic problem but whose presentation is
slightly different from books dealing with traditional photogrammetry. In
§1.1 there are also some considerations about atmospheric refraction, the
distortion due to the optics, and a few rules of thumb in planning aerial
missions where digital images are used. In §1.2, we present some radiometric
impacts of the atmosphere and of the optics on the image, which
helps to understand the very physical nature of the aerial images. And in
§1.3, these few lines about colorimetry are necessary to understand why
the digital tools for managing black and white panchromatic images need
not be the same as the tools for managing colour images. Then we will
present the instruments used to obtain the images, digital of course. In
§1.4 we will consider the geometric constraints on optical image acquisitions
(aerial, and satellite as well). From §1.5 to §1.8, the main digital
acquisition devices will be presented, CCD cameras (§1.5), radars (§1.6),
airborne laser scanners (§1.7), and photographic image scanners (§1.8).
And we will close this chapter with an analysis of the key problem of the
size of the pixel, and the signal-to-noise ratio in the image.

2 Yves Egels
1.1 MATHEMATICAL MODEL OF THE GEOMETRY OF
THE AERIAL IMAGE
Yves Egels
The geometry of images is the basis of all photogrammetric processes,
analogical, analytic or digital. Of course, the detailed geometry of an image
essentially depends on the physical features of the sensor used. In analytic
photogrammetry (the only difference with digital photogrammetry is the
digital nature of the image) the use of this technology of image acquisition
requires therefore a complete survey of its geometric features, and of
the mathematical tools expressing the relation between the coordinates on
the image and those of ground points (and, if the software is correct, this
will be the only thing to do).
We shall explain here, just as an example, the case of the traditional
conical photography (the image being silver halide or digital), that is still
today the most used and that will be able to be a guide for the analysis
of a different sensor. The leading principle, here as well as in any other
geometrical situation, is to approach the quite complex real geometry
by a simple mathematical formula (here the perspective) and to consider
the differences between the physical reality and this formula as corrections
(‘corrections of systematic errors’) presented independently. The imaging
devices whose geometry is different are presented later in this chapter
(§§1.4 to 1.7).
1.1.1 Mathematical perspective of a point of the space
The perspective of a point M of the space, of centre S, on the plane P is
the intersection m of the line SM with the plane P. Coordinates of M will
be expressed in the reference system (O, X, Y, Z), and the ones of m in
the reference system of the image (c, x, y, z). The rotation matrix R corresponds
to the change of system (O, X, Y, Z) → (c, x, y, z). One will note
F the coordinates of the summit S in the reference of the image.
M XM YM ZM S XS YS ZS F xc yc m image of M ⇔ Fm → .SM → .
p m x
y
If one calls K the vector unit orthogonal to the plane of the image one
can write:
0
m ∈ picture ⇔ Kt K
m 0 that implies ’
tF K t R(M S)

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X
m
Z
O
from where the basic equation of the photogrammetry, so-called collinearity
equation:
m F . (1.1)
This equation can be developed and reordered according to coordinates
of M, under the so-called ‘11 parameters equation’, which appears simpler
to use, but should be handled with great care:
KtFR(M S)
K t R(M S)
x a 1X M b 1Y M c 1Z M d 1
a 3 X M b 3 Y M c 3 Z M 1
K
z
c
F
S
Y
y
x
The geometry of the aerial image 3
Figure 1.1.1 Systems of coordinates for the photogrammetry.
R
M
y a 2X M b 2Y M c 2Z M d 2
a 3 X M b 3 Y M c 3 Z M 1
. (1.2)

4 Yves Egels
1.1.2 Some mathematical tools
1.1.2.1 Representation of the rotation matrixes, exponential and
axiator
In computations of analytic photogrammetry, the rotation matrixes appear
quite often. On a vector space of n dimensions, they depend on n(n 1)/2
parameters, but do not form a vector sub-space. There is therefore no
linear formula between a rotation matrix and its ‘components’. It is,
however, vital to be able to express such a matrix judiciously according
to the chosen parameters. In the case of R3 , it is usual to analyse the rotation
as the composition of three rotations around the three axes of
coordinates (angles w, and , familiar to photogrammetrists). But the
resulting formulas are laborious enough and lack symmetry, which obliges
us to perform unnecessary developments of formulas. One will be able to
define a rotation of the following manner physically: rotation of an angle
around a unitary vector
→ a
b
c , with (√a2 b2 c2 = 1)
We will call here the axiator of a vector the matrix equivalent to a vectorial
product:
→ ∧ V → ~ ·V
one will check that
~ 0
c
b
. (1.3)
It is easy to control that the previous rotation can be written: R e ~ .
Indeed,
, (1.4)
therefore, since ~ · → ∧ → 0 (a well-known property of the vectorial
product) e ~ → →
·. is the rotation axis, only invariant. One will
check that ~ e
~ ~ 3 4 , 2, ~ ~ t etc.; on the other hand, ~ ~
. . . ~ n n
. . .
n!
(e ~ )
c
0
a
b
a
0
~ t . . . ~ t n
n!
n
. . .

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(1.5)
.
Therefore this matrix is certainly an orthogonal matrix, which is a rotation
matrix as det R 1 (as ~ e
~ t ). One will also verify that the rotation
angle is equal to , for example by computing the scalar product of a
normal vector to with its transform.
One sees therefore, while regrouping the even terms and the odd terms
of the procedure:
~ (e ~ 1 )
R ~ ~ 3
~ . . . (1) ~ n n
R I . (1.6)
~ sin ~ 2 (1 cos ) (Euler formula)
This formula will permit a very comfortable calculation of rotations. Indeed
one can choose, as parameters of the rotation, the three values a, b and
c. One can then write:
→ →
Θ . (1.7)
a
c and thus ||Θ→ ||, → Θ→
b
If one expresses sin and cos using tan /2 with the help of the classic
trigonometric formulas, it becomes:
R (I . (1.8)
~ tan (/2)) 1 (I ~ tan (/2)) (Thomson formula)
1.1.2.2 Differential of a rotation matrix
Expressed under this exponential shape, it is possible to differentiate the
rotation matrixes. One may determine:
dR ≈ e Θ~ dΘ ~ R dΘ ~
3! . . . ~ 2 2
2! ~ 2 4
4!
The geometry of the aerial image 5
n!
. . .
. . .
. (1.9)
In this expression, the differential makes the parameters of the rotation
appear under matrix shape, which is not very practical. Applied to a vector,
it can be written (using the anticommutativity of the vectorial product):
dR·A R·dΘ . (1.10)
~ ·A R·A ~ ·dΘ

6 Yves Egels
1.1.2.3 Differential relation binding m to the parameters of the
perspective
The previous equation is not linear, and to solve systems corresponding
to analytical photogrammetry (orientation of images, aerotriangulation),
it is necessary to linearize them. Variables that will be taken into account
are F, M, S and R.
If one puts A M S and U RA
(1.11)
dU R(dM dS) dRA R(dM dS A ~ dm dF
d). (1.12)
KtdF U
KtU KtF KtU KtFUKt (Kt 2 U) dU
On the other hand, K t F being a scalar, K t FU UK t F and K t dFU UK t dF.
One then gets:
dm . (1.13)
If one writes
KtU UKt (KtU) 2 [KtU dF KtFR(dM dS A ~ dΘ)]
p KtF, U u1 u2 u3 and V u3 0 0
u3 one gets after manipulation:
dx V
dy u3 dF p
2 u3 . (1.14)
Under this matrix shape, the computer implementation of this equation
requires only a few code lines.
1.1.3 True geometry of images
u 1
u 2 ,
p
VR(dS dM) 2 u3 VR A~ dΘ
In physical reality, the geometry of images only reproduces in an approximate
way the mathematical perspective whose formulas have just been
established. If one follows the light ray from its starting point on the
ground until the formation of the image on the sensor, one will find a
certain number of differences between the perspective model and the reality.
It is difficult to be comprehensive in this area, and one will mention here
only the main reasons for distortion whose consequences are appreciable
in the photogrammetric process.

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1.1.3.1 Correction of Earth curvature
The first reason for which photogrammetrists use the so-called correction
of Earth curvature in photogrammetry is that the space in which cartographers
operate is not the Euclidian space in which the collinearity
equation is set up. It is indeed in a cartographic system, in which the
planimetry is measured in a plane representation (often conform) of the
ellipsoid, and the altimetry in a system of altitudes.
The best solution for dealing with this is to make rigorous transformations
from cartographic to tridimensional frames (it is usually more
convenient to choose a local tangent tridimensional reference, if it is necessary
just to write relations of planimetric or altimetric conversion in a
simple way). This solution, if better in theory, is, however, a little difficult
to put into an industrial operation, because it requires having a
database of geodesic systems, of projection algorithms (sometimes bizarre)
used in the client countries, and arranging a model of the zero level surface
(close to the geoid) of the altimetric system concerned.
An approximate solution to this problem can nevertheless be found, that
is – experience proves it – of comparable precision with the precision of
this measurement technique. It relies on the fact that all conform projections
are locally equivalent, with only a changing scale factor. One can
attempt to replace the real projection, in which is expressed the coordinates
of the ground, by a unique conform projection therefore (and why
not try for simplicity!), for example a stereographic oblique projection of
the mean curvature sphere on the tangent plane to the centre of the work.
The mathematical formulation then becomes as shown in Figure 1.1.2
(the figure is made in the diametrical plane of the sphere containing the
centre of the work A and the point I to transform).
I is the point to transform (cartographic), J the result (tridimensional),
I′ the projection of I on the plane and J′ the projection of J on the terrestrial
sphere of R radius. I′ and J′ are the inverse of each other in an
inversion of B pole and coefficient 4R2 .
Let us put:
I x
Rh I′ x
R J′ x′
y′ J (1 ) x′
y′
The calculation of the inversion gives:
||BI′|| · ||BJ′|| 4R 2
BJ′ BI′
J′ B B′ x(12 )
4R2
⇒ 2
BI′
The geometry of the aerial image 7
x
1
2 ≈ 1 2
1
R(12 2 ) J (12 )(1)x
(12 2 )(1)R
2R
h
.
R
(1.15)

8 Yves Egels
O
JI (2 )x
2 2 R
. (1.16)
One can consider that J I corresponds to a correction to bring us to the
coordinates of I:
I curvature xh/Rx3 /4R 2
x 2 /2R
B
A
R
Figure 1.1.2 Figure made in the diametrical plane of the sphere containing the
centre of the work A and the point I to transform.
.
J′
(1.17)
In the current conditions, the term of altimetric correction is by far the
most meaningful. But for aerotriangulations of large extent, planimetric
corrections can become important, and must be considered. If the aerotriangulation
relies on measures of an airborne GPS (global positioning
system), it is necessary not to forget also to do this correction on coordinates
of tops, that also have to be corrected for the geoid–ellipsoid
discrepancy.
1.1.3.2 Atmospheric refraction
Before penetrating the photographic camera, the luminous rays cross the
atmosphere, whose density, and therefore refractive index, decreases with
the altitude (see Table 1.1.3).
h
J
I'
I
h
x

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This variation of the index provokes a curvature of the luminous rays
(oriented downwards) whose amplitude depends on atmospheric conditions
(pressure and temperature at the time of the image acquisition), that
are not uniform in the field of the camera, and are generally unknown.
Nevertheless, this deviation is small with regard to the precision of photogrammetric
measurements (with the exception of very small scales). It will
thus be acceptable to correct the refraction using a standard reference
atmosphere: in order to evaluate the influence of the refraction, it will be
necessary to use a model providing the refraction index at various altitudes.
Numerous formulas exist allowing an evaluation of the variation of the
air density according to altitude. No one is certainly better that any other,
because of the strong turbulence of low atmospheric layers. In the tropospheric
domain (these formulas would not be valid if the sensor is situated
in the stratosphere), one will be able to use, for example, the formula
published by the OACI (Organisation de l’Aviation Civile Internationale):
where
n n 0 (1 ah bh 2 ), (1.18)
a 2.560.10 8 , b 7.5.10 13 , n 0 1.000278 h in metres,
or this one, whose integration is simpler:
where
n 1 ae bh , (1.19)
a 278.10 6 , b 105.10 6 .
The geometry of the aerial image 9
Table 1.1.3 Atmospheric co-index of refraction–variations with the altitude
H (km) 1 0 1 3 5 7 9 11
N (n1)·10 6 306 278 252 206 167 134 106 83
The rays appear to come then from a point situated in the extension of
the tangent to the ray at the entrance into the optics, thus introducing a
displacement of the image.
The calculation of the refraction correction can be performed in the
following way: the luminous ray coming from M seems to originate from
the point M′ situated on one same vertical, so that MM′ y. One will
modify the altitude of the object point M by the correction y by putting
it in M′. This method of calculation has the advantage of not supposing

10 Yves Egels
M′
M
y
that the axis of the acquired image is vertical, and thus works also in
oblique terrestrial photogrammetry. (See Figure 1.1.4.)
dy h hM dv ,
sin v · cos v
from where
S
y MM′ M
. (1.20)
The formula of Descartes gives us the variation of the refraction angle:
n · sin v cte,
or dn sin v n cos v dv 0,
or again
d
S
h
v
Figure 1.1.4 Optical ray in the atmosphere (with a strong exaggeration of the
curvature).
h h M
sin v · cos v
dv . (1.21)
In the case of photography of a zone of small extension, one will suppose
the Earth to be flat, the vertical (and the refractive index gradients) are
dn
tan v
n
x

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therefore all parallel to each other (this approximation is not valid in
spatial imagery). The radius being very large, one will be able to assimilate
the bow and the chord, the v angle and the refractive index can be
considered constant for the integration.
MM′
S
M
S 1
(h h .
M) (1.22)
dn
dh dh
cos2 v M
With this second formula for refraction, the calculation for the complete
rays gives:
dn
dh ab ebh , dn
dh dh a ebh n 1
and
h .
(1.23)
If one puts D ||SM|| and H hS hM one gets the following refraction
correction:
dn
dh dh 1
h (n 1) b
y D2
H2 nS nM H(nS 1) b
.
(1.24)
For aerial pictures at the 1/50,000th scale with a focal length of 152 mm,
this correction is of about 0.20 m to the centre, and reaches 0.50 m at
the edge of the image. It is appreciably less important at larger scales for
the same focal length.
This formula also permits either the correction of refraction with oblique
or horizontal optical axes lines (terrestrial photogrammetry), which are
very obviously not acceptable domains in very commonly used formulas,
bringing a radial correction to the image coordinates. One will be able to
verify that when h M → h S, the limit of y is:
y H n S 1 b
2 D2 ,
(h hM) sin v
sin v · cos v cos v dn
n
The geometry of the aerial image 11
S
M
(h hM) cos 2 v dn
n
the classical refraction formula for a horizontal optical axis.

12 Yves Egels
1.1.3.3 At the entrance in the plane
In a pressurized plane two phenomena may occur. First, the light ray
crosses the glass plate placed before the objective. This glass plate, therefore
of weak thermal conductivity, is subject to significant temperature
differences and bends under the differential dilation effect (in the opposite
direction to the bending due to the pressure difference, that induces
a much smaller effect). It takes a more or less spherical shape, and operates
then like a lens that introduces an optic distortion. Unfortunately, if
the phenomenon can be experimentally tested (and the calculation shows
that its influence is not negligible), it is practically impossible to quantify
it, the real shape of the glass plate porthole depends on the history of the
flight (temperatures, pressures inside and outside). There are techniques
of calculation that will be applied to §1.1.3.6, however, (a posteriori
unknowns) permitting one to model and to eliminate the influence of it
in the aerotriangulation.
When the plane is pressurized the luminous ray is refracted a second
time at the entrance to the cabin, where the pressure is higher than that
outside at the altitude of flight (the difference in pressure is a function
of the airplane used). One can model this refraction in the same way as
for the atmospheric refraction (the sign is opposed to the previous one,
because the radius arrives in a superior index medium).
While noting nc the refractive index inside the cabin, and while supposing
that the porthole is horizontal,
dv (n c n s ) tan v (n c n s ) R
H
dy D2
H 2 (n c n s)H.
(1.25)
(1.26)
While combining this equation with that of atmospheric refraction, one
sees that it is sufficient to replace the altitude of the top by the altitude
of the cabin in the second part:
y D2
H2 nS nM H(nc 1) b
.
(1.27)
Thus we have to compute the cabin index of refraction. Often in pressurized
planes, the pressure is limited to a maximal value of P max (for
example 6 psi 41,370 Pa for the Beechcraft King Air of IGN-F) between
inside and outside. Under a given altitude limit (around 4,300 m in the
previous example), the pressure is kept to the ground value. The refractive
index n and co-index N are linked to the temperature and pressure
by an approximate law:

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N (n 1)106 790 , P in kPa and T in K.
The temperature decreases with the altitude with an empirical variation T
T0 6.5 × 103 P
T
Z. If one takes TC T0 298 K, the cabin refractive
index will be:
N C N S (1 2.22 × 10 5 Z S) 2,696 P.
The geometry of the aerial image 13
This index will be limited to its ground value (N 278 in this model),
if the altitude is below the pressurization limit. One may note that, in
current flight conditions (flight altitude 5,000 m, pressurization limit
4,300 m), this total correction is nearly the opposite of the correction
computed without cabin pressurization.
1.1.3.4 Distortion of the optics
In elementary optics (conditions of Gauss: thin lenses, rays with a low tilt
angle with respect to the optical axis, low aperture optics), all rays passing
through the centre of the objective are not deviated. This replicates the
mathematical perspective. Unfortunately, the real optics used in photogrammetric
image acquisitions do not fulfil these conditions.
In the case of perfect optics (centred spherical dioptres) the entrance
ray, the exit ray, and the optical axis are coplanar. But the incident and
emergent rays are not parallel. This gap of parallelism constitutes the
distortion of the objective. It is a permanent and steady characteristic of
the optics, which can be measured prior to the image acquisitions, and
corrected at the time of photogrammetric calculations.
The measure of this distortion can be achieved on an optical bench,
using collimators, or by observation of a dense network of targets through
the objective. Manufacturers, to provide certification of the aerial camera
that they produce, use these methods, which are quite complicated and
costly. It is also possible to determine the distortion (as well as the centring
and the principal distance) by taking images of a tridimensional polygon
of points very well known in coordinates, and by calculation of the
collinearity equations, to which one adds unknowns of distortion according
to the chosen model.
In the case of perfect optics, the distortion is very correctly modelled
by a radial symmetrical correction polynomial around the main point of
symmetry (intersection of the optic axis with the plane of the sensor).
Besides, one can demonstrate easily that this polynomial only contains
some terms of odd rank. The term of first degree can be chosen arbitrarily,
because it is bound by choice of the main distance: one often takes it as
a null (main distance to the centre of the image) or so that the maximal
distortion in the field is the weakest possible.

14 Yves Egels
If the optics cannot be considered as perfect (it is sometimes the case if
one attempts to use cameras designed for the general public for photogrammetric
operations), the distortion can lose its radial and symmetrical
character, and requires a means of calibration and more complex modelling.
Besides, in the case of zooms (that one should avoid . . .), this distortion
does not remain constant in time because of variations of centrage brought
about by the displacement of the pancratic vehicle (mobile part permitting
the displacement of lenses). Any modelling then becomes very uncertain.
1.1.3.5 Distortions of the sensor
The equation of the perspective supposes that the sensor is a plane, and
that one can define there a reference of fixed measure. Thus, it will be
necessary to compare the photochemical sensors (photographic emulsion)
and the electronic sensors (CCD matrixes). These last are practically indeformable,
and the image that they acquire is definitely steady (in any case
on the geometric plane). The following remarks will therefore apply to the
photochemical sensors only.
The planarity of the emulsion was formerly obtained by the use of photographic
glass plates, but this solution is no longer used, except maybe in
certain systems of terrestrial photogrammetry. It was, besides, not very
satisfactory. Today one practically always uses vacuum depression of the
film on the plate at the bottom of the camera. This method is very convenient,
provided that there is no dust interposed between the film and
the plate, which is unfortunately quite difficult to achieve. There follows
a local distortion of the image, which is difficult to detect (except in radiometrically
uniform zones, where there appears an effect of shade) and
impossible to model.
The dimensional stability of the image during the time, if it is improved
with the use of so-called ‘stable’ supports, is quite insufficient for the use
of photogrammetrists. Distortions ten times better than the necessary
measurement precision are frequent. The only efficient counter-measure is
the measure of the coordinates on the images of well-known points (reference
marks of the bottom plate of the camera) and the modelling of the
distortion by a bidimensional transformation. One usually chooses an
affinity (general linear transformation) that represents correctly the main
part of the distortion. But this distortion is thus measured only on the side
of the image, in a limited number of points (eight in general). The interpolation
inside the image is therefore of low reliability.
1.1.3.6 Modelling of non-quantifiable defects
The main corrections to apply to the simplistic model of the central perspective
have been reviewed. Several of them can be considered as perfectly
known – the curvature of the Earth for example; others can be calculated

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roughly: refraction, distortion of the film, and others that are completely
unknown, the distortion of the porthole glass plate, for example.
When the precise geometric reconstitution is indispensable – as is notably
the case in aerotriangulation, where the addition of systematic errors can
generate intolerable imprecision – a counter-measure consists in adding to
the equation of collinearity and its corrective terms a parametric model
of distortion (often polynomial). This model contains a small number of
parameters, chosen in order to best represent influences of no directly
modelizable defects. These supplementary a posteriori unknowns of systematism
will be solved simultaneously with the main unknowns of the
photogrammetric system, which are coordinates of the ground points, tops
of images, and rotations of images. This technique usually permits a gain
of 30 to 40 per cent on altimetric precision of the aerotriangulation.
1.1.4 Some convenient rules
The geometry of the aerial image 15
Rules for the correct use of aerial photogrammetry have been known for
several decades, and we will therefore only briefly recall the main features.
Besides, variables on which one can intervene are not numerous. This
arises essentially from the necessary precision, which can be specified in
the requirements. They can also be deduced from the scale of the survey
(even though this one is digital, one can assign it a scale corresponding to
its precision, that is conventionally 0.1 mm to the scale). The practice
shows that the errors that accumulate during the photogrammetric process
limit its precision – in the current studies – to about 15 to 20 microns on
the image (on the very well-defined points) for each of the two planimetric
coordinates. This number can be improved appreciably (down to 2 to
3 m) by choosing some more coercive operative (and simultaneously
costlier) ways to work. For the altimetry, this number must be grosso
modo divided by the ratio between the basis (distance between points of
view) and the distance (of these points of view to the photographed object).
This ratio depends directly on the chosen field angle for the camera: the
wider the field, the more this ratio will increase, the more the altimetric
precision will be close to the planimetric precision. As an example, Table
1.1.5 sums up the characteristics of the most current aerial camera values
(in format 24 × 24 cm) with values of standard base length (overlap of
55 per cent).
Knowing the precision requested for the survey, it is then very simple
to determine the scale of the images. The choice of the focal distance will
be guided by the following considerations: the longer the focal distance,
the higher the altitude of flight will be, the more the hidden parts will be
reduced (essentially feet of buildings in city, not to mention complete
streets), but simultaneously the more the altimetric precision is degraded,
and the more marked the radiometric influence of the atmosphere.

16 Yves Egels
Table 1.1.5 Characteristics of the most current aerial camera values
(in format 24 × 24 cm) with values of standard baselength
(overlap of 55 per cent)
Focal length 88 mm 152 mm 210 mm 300 mm
Field of view 120° 90° 73° 55°
B/H 1.3 0.66 0.48 0.33
Flight height (1/10,000) 880 m 1520 m 2100 m 3000 m
Planimetric precision (1/10,000) 20 cm 20 cm 20 cm 20 cm
Altimetric precision (1/10,000) 15 cm 30 cm 40 cm 60 cm
In practice, one will preferentially use the focal distance of 152 mm.
Shorter focal lengths will be reserved for the very small scales, for which
the altitude of flight can constitute a limitation (the gain in altimetric precision
is actually quite theoretical, as the mediocre quality of the optics
makes one lose what was gained in geometry). A long focal distance will
be preferred most of the time for the orthophotographic surveys in urban
zones, in which the loss of altimetric quality is not a major handicap. In
the case of a colour photograph, it will be necessary nevertheless to take
care of the increase of the atmospheric diffusion fog (due to a thicker
diffusing layer), which will especially have the consequence of limiting the
number of days when it is possible to take the images. Another way (less
economic) to palliate the hidden part problem is to use a camera with a
normal focal distance, while choosing more important overlaps: one can
reconcile a good altimetric precision, a weak atmospheric fog, and acceptable
distortions for objects on the ground.
1.2 RADIOMETRIC EFFECTS OF THE ATMOSPHERE
AND THE OPTICS
Michel Kasser
1.2.1 Atmospheric diffusion: Rayleigh and Mie diffusions
The atmosphere is generally opaque to the very short wavelengths, its
transmission only starting toward 0.35 m. Then, the atmosphere presents
several ‘windows’ until 14 m, the absorption becoming again practically
total between 14 m and 1 mm. Finally, the transmission reappears
progressively between 1 mm and 5 cm, to become practically perfect to
the longer wavelengths (radio waves).
The low atmosphere, in the visible band, is not perfectly transparent,
and when it is illuminated by the Sun it distributes a certain part of the

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Radiometric effects of the atmosphere, optics 17
radiance that it receives: all of us can observe the milky white colour of
the sky close to the horizon, and to the contrary its blue colour is very
marked in high altitude sites towards the zenith. These luminous emissions
are important data to understand correctly the images used in
photogrammetry, and in particular the diffuse lighting coming from the
sky in zones of shades, or again the atmospheric fog or white-out and its
variation according to the altitude of image acquisition. We will start with
a presentation of the present diffusion mechanisms in the atmosphere, to
assess the effects of this diffusion on the pictures obtained from an airplane
or a satellite.
1.2.1.1 Rayleigh diffusion
The diffusion by the atmospheric gases (often called absorption, in an erroneous
way, since the luminous energy removed from the light rays is merely
redistributed in all directions, but not transformed into heat) is due to the
electronic transitions or vibrations of atoms and molecules generally present
in the atmosphere. On the whole, the electronic transitions of atoms
provoke a diffusion generally situated in the UV (these resonances are very
much damped because of the important couplings between atoms in every
molecule, and thus the effect is still noticeable even at much lower frequencies),
whereas vibration transitions of molecules rather provoke diffusions
situated at lower frequencies, and therefore in the IR (and these are sharp
resonances, because there is nearly no coupling between the elementary
resonators that are molecules, and therefore the flanks of bands are very
stiff). The Rayleigh diffusion, particularly important to the high optical
frequencies, corresponds to these atomic resonances. We have therefore a
factor of attenuation of a light ray when it crosses the atmosphere, and
at the same time a substantial source of parasitic light, since light removed
from the incidental ray is redistributed in all directions, so that the atmosphere
becomes a secondary light source.
In short, Rayleigh diffusion is characterized by two aspects:
• its efficiency varies as 4 , which combined with the spectral sensitivity
of the human eye is responsible of the blue appearance of the sky;
• the diagram of light redistributed is symmetrical between the before
and the rear, with a front or rear diffusion twice as important as the
lateral one.
This diffusion may thus be very satisfactorily and accurately modelled.
1.2.1.2 Diffusion by sprays (Mie diffusion)
One calls sprays all particles, droplets of water, dusts that are continuously
sent into the atmosphere by wind sweeping soil, but that can come also

18 Michel Kasser
Table 1.2.1 Typical particle size in
various sprays
Smoke 0.001–0.5 m
Industrial smoke 0.5–50 m
Mist, dust 0.001–0.5 m
Fog, cloud 2–30 m
Drizzle 50–200 m
Rain 200–2000 m
from the sea (particles of salt), from volcanoes because of cataclysmic explosions,
from human activities (industrial pollution, cars, forest fires, etc.) and
also from outside of our globe: meteoroids and their remnants. The essential
characteristic of these sprays, since such is the generic name that one
usually gives to all of these non-gaseous components of the atmosphere, is
that their distribution is at any instance very variable with the altitude (presenting
a very accentuated maximum to the neighbourhood of the ground)
but also very variable with the site and with time. (See Table 1.2.1.)
In fact, every spray distributes light, in the same way that gaseous
molecules do. However, an important difference is that molecules present
some weaker dimensions than the wavelength of light that interests us
here. This implies that the Rayleigh diffusion by molecules (or atoms)
is more or less isotropic. To the contrary, the diffusion by sprays, whose
dimensions are often the same order as the wavelengths considered,
present strong variations with the direction of observation. At the same
time, the intensity of the diffusion by sprays – also called the Mie
diffusion, depends strongly on the dimension of the diffusing particle.
The exact calculation is of limited value, since in practice the quantity of
sprays in the atmosphere is very variable according to the altitude, and
also especially according to the time. In any case, it is generally not possible
to foresee it.
In practice, it is to the contrary from luminous diffusion measurements
that one may measure the density (in number of particles/cm 3 ) of sprays
according to the altitude.
Table 1.2.2 provides some figures, but it is necessary to note that
this distribution is reasonably steady only to an altitude over 5 km. In
the first kilometres of the atmosphere, to the contrary, the influence of
wind, of human activities is such that numbers in the table are only indicative.
The Mie diffusion is characterized by a directional diagram that varies
markedly with the size of sprays. For the very small particles compared
to the wavelength, the diagram is very similar to that of Rayleigh diffusion.
For larger particles, it becomes more and more dissymetric between front

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Table 1.2.2 Typical spray density vs.
altitude
h Sprays density
(km) (particles per cm 3 )
0 200
1 87
2 38
3 16
4 7.2
5 3.1
6 1.1
7 0.4
8 0.14
9 0.05
Radiometric effects of the atmosphere, optics 19
and rear, to give a retrodiffusion negligible compared to the importance
of the front diffusion. (See Figure 1.2.3.)
To assess the importance of the phenomenon on aerial image acquisitions,
one determines the attenuation of a light ray travelling upwards,
from the observed horizontal attenuation, which is obviously more accessible.
One characterizes it by the ‘meteorological visibility’ V, that is the
distance to which the intensity of a collimated light ray of 0.555 m
(wavelength of the maximum sensitivity the eye) falls to 2 per cent of its
initial value. Under these conditions, the practice shows that the diffusion
that comes with the attenuation removes all observable details of the
observed zone, that melts in a uniform grey colour.
R = 0.05 µm, scale × 0.003
θ
R = 0.1 µm, scale × 3
R = 0.5 µm, scale × 1000
Figure 1.2.3 Angular distribution of the Mie diffusion for a wavelength of
0.5 m and for three particle sizes: 0.05, 0.1 and 0.5 m.

20 Michel Kasser
The reduction of intensity of a light ray depends, physically, on the
number of particles interacting with it, the resulting attenuation being
correctly described by Beer’s law:
I I 0 e kx , (1.28)
where x is the distance in the absorbing medium, and k the coefficient of
absorption.
The visibility V, easily appreciated by a trained observer, allows the
calculation K M K R and therefore the part of attenuation due to sprays,
by the difference between the observed coefficient K obs (such as: e K obsV
0.02) and the one K R easy to calculate, resulting from Rayleigh diffusion.
I I 0 e (K R K M ) x I 0 e K R x e K M x .
(1.29)
From the visibility V, one establishes in an experimental way the coefficient
of attenuation for different wavelengths. This leads to the formula
(in km 1 , for in m and V in km):
K M 3.91
V 0.555
0.585V1/3
. (1.30)
Table 1.2.4 gives the numeric figures for various wavelengths.
If one wants to switch from the horizontal attenuation to the vertical
attenuation, to assess the effect on a light ray going from the ground to
a plane, one admits besides that the density of sprays, according to the
altitude, follows an exponential law. Figure 1.2.5 shows the relation
between the coefficient of extinction (that is the k coefficient of Beer’s law)
and the visibility.
Figure 1.2.6 illustrates the result of the integration calculation for a vertical
crossing of the diffusing layer, done for an attenuation K M 10 3 km 1 at
h 5 km (altitude over which the concentration of sprays stops being influenced
considerably by ground effects, and may be considered as constant).
Table 1.2.4 Variations of the Mie and Rayleigh coefficients of attenuation
at various wavelengths for three values of the ground
meteorological visibility
(m) K Rayleigh K Mie
(km 1 ) (km 1 )
V 1 km V 5 km V 10 km
0.4 0.044 4.7 1.1 0.58
0.6 0.0083 3.7 0.72 0.35
0.8 0.0026 3.1 0.54 0.24
1.0 0.0006 2.8 0.43 0.18

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Altitude (km)
7
5
3
1
V = 10 km
V = 6 km
V = 2 km
Radiometric effects of the atmosphere, optics 21
0.01 0.1 1
KM coefficient at 0.555 µm in km –1
Figure 1.2.5 Variations of the coefficient of attenuation at 0.555 m for three
values of the ground meteorological visibility.
Optical
transmission in %
100
80
1
60
0.6
40
20
0.2
10 0.1
2 4 6 8 10 12(km)
Meteorological visibility at ground level
One should also note that, in the visible domain, the content of water
vapour does not change the visibility.
1.2.2 Effects of the atmospheric diffusion in aerial image
acquisition
The diffusion of light by atmospheric gas molecules and by all sorts of
sprays dispersed in the atmosphere is not only responsible for the light
attenuation. In fact, the portion of atmosphere crossed by the light rays
of observation behaves, when it is illuminated by the Sun, like a luminous
source whose radiance arrives in part on the detector.
2
Total optical density
through the layer
of concentration
of sprays (0–5 km)
Figure 1.2.6 Optical transmission and optical thickness for a vertical crossing of
the diffusing layers for various values of meteorological visibility at
ground level.

22 Michel Kasser
Being foreign to the ground that one generally intends to observe, this
radiance can be qualified as ‘parasitic’, and constitutes one of the main
sources of ‘noise’ in image processing in the visible domain. This diffusion
is as difficult to calculate as the corresponding attenuation, as like it,
it depends on distribution by sizes and by the nature of diffusing particles.
And moreover it depends, in the case of sprays whose size is not
negligible in comparison to , on the angle between the direction of observation
and the direction of lighting. The contribution of the Rayleigh
diffusion, especially important to the short wavelengths, is therefore the
only one easy to calculate.
It remains to determine the fraction of this flux sent back towards the
instrument of observation. To a first approximation, one will be able to
admit that the diffusion is isotropic. The diffusion (sum of contributing
diffusions Mie and Rayleigh) intervenes finally in the three following aspects:
• Lighting brought by the sky in zones to the shade, diffuse source that
includes at least the Rayleigh diffusion, and that is therefore more
important in the blue, but that is in any case characteristic of the shade
contrast. If this contrast is strong, it means that shades are poorly illuminated,
and therefore that the diffusion is weak. The lower the Sun
is on the horizon, the weaker the direct solar lighting and the more
the atmospheric diffusion becomes predominant. On an indicative
basis, between a surface exposed to the Sun and the same surface in
the shade, the typical lighting differences are of: 2 (Sun to 20° on the
horizon, sky misty enough, V 2 km), 3 (Sun to 45°, V 5 km),
10 (extreme case, very high Sun and V > 10 km, frequent case, for
example, in high mountains).
• Attenuation of the useful light ray going from the illuminated ground
towards the device used for image acquisitions. This attenuation
depends on the height of flight H and the value of V. For example
for H > 4 km, the attenuation is the same as that of the direct solar
radiance, and it may range from a value of transmission of 0.90 (V
10 km, for example) to 0.70 (V 3 km) or even less. And for the
lower flight heights, the exponential decrease of K with the increasing
altitudes shows that this coefficient is near unity for the low flights
(large scales, H 1,500 to 2,000 m). On the other hand, for values
of H > 4 or 5 km, the attenuation is the same as for an imaging satellite.
• Superposition of a reasonably uniform atmospheric fog or white-out
on the useful picture formed in the focal plane. This parasitic luminous
flux can be computed according to the following way in the case
where the plane is entirely over the diffusing layer (H > 4 or 5 km):
(1) the diffusion is reasonably symmetrical fore/rear; (2) this diffusion
essentially originates from the light removed from the direct solar rays,
between 10 per cent and 50 per cent according to our previous remarks;

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Radiometric effects of the atmosphere, optics 23
(3) the half of this flux going upwards therefore represents the source
of light, coming from all the lower half-space, the other half going
downwards; (4) one makes the hypothesis that this flux is isotropic in
all this half-space and one calculates, considering the aperture of the
camera, the flux F that enters there from all this half-space; (5) one
calculates the solid angle under which is seen a pixel on the ground
by the camera; (6) one finally corrects F of the ratio formed by this
solid angle and 2 (solid angle formed by a half-space). This figure
for the flux will be reduced if the plane flies lower, as mentioned previously,
but one is generally surprised when one does this calculation,
as the atmospheric fog is so important as compared to the useful signal.
In current conditions, for H > 5 km the energy from the atmospheric
fog is frequently more than the energy of the useful image, which
almost always gives to the uncorrected colour pictures a milky white
aspect that makes the appearance of colours often disappear to a large
extent.
1.2.3 Radiometric problems due to the optics
In the optic energy calculations that one does in aerial imagery, it is necessary
to also take into account the classic effects due to camera optics. We
have been used, with traditional aerial cameras, to seeing these defects
corrected in a quasi-perfect way, essentially because the downstream photogrammetric
chain was unable to correct any radiometric defect of the
optics. The digital image acquisitions using a CCD permit one to deal with
these problems very correctly even with much cheaper and readily available
materials, optimized for the quality of the picture, and not for typically
photogrammetric aspects such as the distortion: these shortcomings are
corrected by calculation. Remarks that follow sum up a few of these points:
• The field curvature is very inopportune, since it implies that the zone
of better focusing is not plane: this defect must therefore be further
reduced if one works with small pixels in the picture plane. For that
reason it is necessary to pay attention to the parallel glass plates in
front of the CCD sensor when one works with a large field, which is
the rule in photogrammetry: this plate leads to an easily observable
radial distortion, although not a troublesome one since it can be
included in the calibration.
• The distortion has inevitably a symmetry of revolution. It is often
described by an odd degree polynomial, and one should not be
concerned by its importance, but rather by the residues observed
between the polynomial and measures of calibration.
• The vignettage is governed by optics in the approximation of Gauss
of a quite appreciable lighting loss of the sensitive surface following
a law in cos 4 of the angle between rays and the optic axis, which

24 Michel Kasser
reduces the brightness greatly within the angles of an image. This effect
is very well corrected today, including optics for the general public,
and can also be radiometrically calibrated in any camera, using an
integrating sphere as a light source.
• The shutter is also an important piece. If it is installed close to the
optic centre of the objective, its rise and fall times do not create a
problem, as at each step of the shutter movement, all the focal plane
receives the same light modulation, but then there is a shutter in each
objective used, which increases their cost. For the digital cameras using
some CCD matrixes, one will note that the very high sensitivity of
these devices requires having access to a very short exposure time,
which is not necessarily feasible in times of strong sunlight, considering
the relative slowness of these mechanical devices. One is then
sometimes obliged to add neutral density filters in front of the objective
to limit the received flux, as it is impossible to effectively close
the diaphragm, which would create excessive diffraction effects.
Otherwise, if one uses a linear movement blade shutter with this type
of camera, it is necessary to check that the scrolling of the window
proceeds in the sense of the transfer of charges of the CCD. And the
electronic compensation of forward motion (against linear blurring
due to the speed of the airplane, often called TDI – see §1.5, that
consists in shifting charges in the focal plane at the same physical
speed as the scrolling of the picture in the focal plane) has to be activated
during the entire length of movement of the blades (generally
1/125th of a second), and not during the time of local exposure of
the CCD (that can range sometimes up to the 1/2,000th of a second).
If the blade movement were oriented in another direction, it would
indeed result in an important distortion of the image. And if its direction
is good but the electronic compensation of forward movement is
not activated at the correct time, there will only be a part of the image
that will be correct, in sharpness and in exposure as well.
• Finally, on digital cameras, it is necessary to note that it is easy to
calibrate the sensitivity of pixels individually, and to apply a systematic
correction, which improves the linearity of the measure. Otherwise,
in the matrix systems, the electronic compensation of forward motion
leads to sharing of the total response over several pixels, which
improves the homogeneity of the pixel response once more.

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1.3 COLORIMETRY
Yannick Bergia, Michel Kasser
1.3.1 Introduction
The word ‘colour’ is a dangerous word because it has very different senses.
We all have one intuitive understanding of this notion, and we think we
know what is green, or orange. In fact, the word ‘colour’ regains two
fundamentally different notions:
• on the one hand, the visual sensation that our eyes receive from the
surface of an illuminated object;
• on the other hand, the spectral curve of a radiance fixing, for every
wavelength, the quantity of light emitted or transmitted by an object.
The first meaning is eminently subjective and dependent on many parameters.
The second is entirely objective: it corresponds to a physical
measure. The fact that the language only proposes one term for these two
notions is a source of confusion. We must always have to mind that our
eyes only communicate to us a transcription of discerned light limiting
itself to the supply of three values, and are not therefore capable of
analysing spectral curves by a large number of points.
The objective of this presentation is to attract the reader’s attention to
the complexity of situations that will be met when some digital processes
are to be applied, not to black and white pictures, but to pictures in colour.
It will especially be the case, in digital photogrammetry, in processes of
picture compression and automatic correlation. It is indeed certain that
for such processes, it has been necessary since the conception of algorithms
to take into account a given type of space colorimetry, and that it is necessary
to choose it in functions, for example, of metrics problems that it
presents.
Colours that our eyes are capable of differentiating, if they are not in
infinite number, are nevertheless extremely numerous. To compare them
or to measure them, one refers to the theoretical basic colours (often called
primary) that are defined as follows. One divides the visible spectrum into
three sub domains, for which one defines colours with a constant radiance
level in all spectral bands:
• between 0.4 and 0.5 microns, the blue;
• between 0.5 and 0.6 microns, the green;
• between 0.6 and 0.7 microns, the red.
Colorimetry 25
A light is said to be blue therefore (respectively, green, red) if it is composed
of equal parts of radiances of wavelengths between 0.4 and 0.5 microns

26 Yannick Bergia and Michel Kasser
(respectively 0.5/0.6, 0.6/0.7 m) and does not contain any other wavelength
of the visible spectrum (one does not consider the remainder of the
spectrum). One also defines, next to these ‘fundamental’ colours, basic
colours called ‘complementary’:
• cyan, whose wavelengths range from 0.4 to 0.6 m;
• magenta, from 0.4 to 0.5 m and 0.6 to 0.7 m;
• yellow, from 0.5 to 0.7 m.
1.3.2 Trichromatic vision
The notion of trichromatic vision is one of the principles basic to
colorimetry. It is based on the fact that the human eye possesses three
types of receptors (cones) sensitive to colour (the eye also possesses other
receptors, short sticks that are sensitive to brightness), each of the three
types of cones having a different spectral sensitivity. This principle applies
in such a way that a colour can be represented quantitatively by only three
values. Besides, experiences prove that three quantities at a time are necessary
and sufficient to specify a colour. Also, they introduce notions of
additivity and proportionality of colours and so confer the intrinsic properties
of a vectorial space of dimension three to all spaces where one would
try to represent colours.
1.3.3 Modelling of colours
To specify a colour means to associate with the spectrum of distribution
of energy of a given light a triplet of values that will represent it in what
will be then a colorimetric space. Considering the results of experiences,
one can consider that providing three colours respecting conditions of
mutual independence (and that will be then the three primary axes of the
space) can be sufficient to define a colorimetric space: for a given colour,
multipliers coefficients of the three intensities of sources associated to
primaries (when the reconstituted colour corresponds to the considered
colour) will be coordinates of the colour in the constructed space. Another
way to express this is to return to the physical data that contains the
colour information and to integrate the spectral distribution of optical
power on the visible wavelengths while using three functions linearly independent
of weighting to define three channels. Thus, one can construct a
colorimetric space, for example the fictive ABC system, by defining three
functions of weighting a(), b(), c() (see Figure 1.3.1). Then every transformations,
linear or not, of such a colorimetric space will also be a
colorimetric space. There are an infinite number of such spaces, but one
will find – in what follows – only certain spaces are often met with.

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a b c
400 700
1.3.4 Survey of classic colorimetric spaces, the RGB, the
HSV and the L*a*b*
1.3.4.1 The RGB space
This is the most often met colorimetric space, used in particular for television
and computer screens, of so-called ‘additive synthesis’ (as opposed
to the ‘subtractive synthesis’ while using white light and subtracting from
it a part of the spectra by filters, which is for example the case in printing,
where each ink acts like a filter on the white paper). Its definition rests
on the choice of three primary colours: the red, the green and the blue.
Considering data processing, the RGB space is represented as a
discretized cube of 255 units of side. All feasible colours for computer
applications are represented therefore by a triplet (R, G, B) of the discrete
space. We may note the first diagonal of the reference frame where colour
is distributed with the same value for the three channels, R, G and B:
it is the axis of the grey or achromatic axis.
This space does not present specific points, but it is the one that the
current material environment imposes on us: the large majority of pictures
in true colours susceptible of being processed is coded in this system. We
will also present methods of conversion from RGB towards another very
common system, the HSV space, this only as an example.
1.3.4.2 The HSV space
⎧
⎪A
=
⎪
⎪
⎨B
=
⎪
⎪
⎪C
=
⎪⎩
Figure 1.3.1 Definition of a fictive colorimetric reference.
Colorimetry 27
a(
λ ) ⋅ P(
λ ) dλ
b(
λ ) ⋅ P(
λ ) dλ
c(
λ ) ⋅ P(
λ ) dλ
Definitions
The Hue, the Saturation and intensity Value that constitute the three
components of this system are the relatively intuitive notions that allow a
better description of the experience of the colour. Some more theoretical
definitions can be given.
λ
700
∫
400
700
∫
400
700
∫
400

28 Yannick Bergia and Michel Kasser
Cyan
Green
Blue
Hue
Yellow
Magenta
Red (Hue = 0)
Figure 1.3.2 Distribution of basis colours on the circle of hues.
The intensity can be presented as a linear measure of the light power
emitted by the object that produces the colour. It allows the dark colours
to be distinguished naturally from the bright ones.
The hue is defined by the CIE (Commission Internationale de l’Éclairage)
as the attribute of the visual perception according to which a zone appears
to be similar to a colour among the red, the yellow, the green and the
blue or to a combination of two of them. It is a way of comparing known
colours on which it is easy to agree. According to this data, colours can
be represented on a circle. The red, the green and the blue are there with
an equal repartition (the red having by convention a null hue). Figure 1.3.2
illustrates this distribution.
The saturation allows the purity of a colour to be determined. It is while
making the saturation vary from a null hue colour, for example, that one
will move from the pure red (most saturated), that can be placed on the
circumference of the hue circle, toward the neutral grey in the centre while
passing all pink tones along the radius of the disk. From a more physical
point of view one can say that if the dominant wavelength of a spectrum
of power distribution defines the hue of the colour, then, the more this
spectrum will be centred around this wavelength, the more the colour will
be saturated.
Considering these definitions, colours specified in the HSV space can be
represented in a cylindrical space and are distributed in a double cone (see
Figure 1.3.3).
Distance in the HSV space
To be able to exploit this space for process applications it is necessary
to define a distance. Naturally, the Euclidian distance does not have any
sense here, the obvious non-linearity of its cylindrical topology and in
particular the discontinuities met in the neighbourhood of the axis of inten-

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t
i
White
s
Black
Red
Figure 1.3.3 Theoretical representation of the HSV space.
sity and the passage of the null hue are unacceptable. One has thus agreed
to consider as a distance between two points in this duplicate cone the
length of the smallest bow of a regular helix that it is possible to draw
between them.
Let us consider two points of the HSV space therefore, P 1 (I 1, T 1, S 1)
and P 2 (I 2 , T 2 , S 2 ). One stands in an orthogonal Euclidian reference frame
whose vertical axis (Z) is confounded with the axis of intensities, and the
first axis (X) is directed by the vector of hue of the point whose intensity
is smallest (suppose that it is P 1 ). One notes I the positive difference of
intensity between the two points (in our case I I 2 I 1 ), S the difference
of saturation (S S 2 S 1 ) and the smallest angular sector defined
by the two angles of hues.
We are then in the situation illustrated by Figure 1.3.4 showing the bow
of helix for which we need to calculate the length precisely. In these conditions
we propose the following parametric representation of this bow:
P(t) X(t) S 1 t S) cos (t)
Y(t) (S 1 t S) sin (t)
Z(t) t I
Colorimetry 29

30 Yannick Bergia and Michel Kasser
Y
Z
θ
The length of the bow is then given by the calculation of the curvilinear
integral
that provides the following result:
D h
S 1
1
Dh 0
S 2
|| ∂P(t)
∂t || dt
1
2 S S 2 √(S 2 I 2 S 2 2 ) S 1 √(S 2 I 2 S 1 2 )
S 2 I 2
P 1
P 2
P(t)
argsh
X
Figure 1.3.4 Portion of helix to compute distances in the HSV colorimetric
system.
S
argsh
1
.
√(S2 I2 )
S2 √(S2 I2
)
(1.31)
Technical way of use of the HSV space
There does not exist a unique HSV space strictly speaking, rather numerous
definitions or derivative specifications. Indeed several quantities deduced
for example from the R, G and B values of a specified colour in the RGB
space can correspond to very subjective definitions of hue, intensity and
saturation that have been given. Conceptually all these spaces are very
much the same in the sense that they all allow one to easily specify a
sensation of colour in terms of hue, intensity and saturation, or if need
be neighbours and equivalent notions.
The most often used definition is that found for example in Gonzales
and Woods (1993): the calculation takes place on the r, v and b values
between 0 and 1 (it is about the R, V and B initial values divided by 255).
If r v b, the considered colour is a nuance of grey, and one imposes
Z
Y
S 1
P 1
P 2
P(t)
X

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by convention: t s 0; it does not affect the reversible character of the
transformation.
(r v) (r b)
2 arc cos 2√(r2
v2 b2 (r v) (r b)
arc cos 2√(r
, if b v
rv vb br) 2 v2 b2 r v b
i ,
3
, if v b
rv vb br)
t (1.32)
s 1
min {r, v, b}
i
.
Colorimetry 31
1.3.4.3 The L*a*b* space
L*a*b*, defined by the CIE in 1976, has the goal of providing a space of
work in which the Euclidian distance has a true sense: it develops a space
uniform to the perception, that is to say in which two greens and two
blues separated by the same distance would lead to the same sensation of
difference for the human eye, which will not be for example the case in
y
0.8
λ = 520 nm
λ = 380 nm
λ = 700 nm
0.8 µm
Figure 1.3.5 Separation of colours in the chromatic L*a*b* diagram.
x

32 Yannick Bergia and Michel Kasser
the RGB system basis as we have a better capability to differentiate in the
blues than in the greens. This affirmation has been verified by the experience
of the chromatic matching of Wyszecki (Wyszecki and Stiles, 1982)
whose results are presented on the chromatic diagram of Figure 1.3.5.
Ellipses that are drawn there (whose size has been exaggerated nevertheless)
represent, according to the position in the diagram, zones whose
colours cannot be discerned by observers.
The transformation toward L*a*b* will distort the space so that these
ellipses become circles of constant radius on the whole of the diagram. It is
this important property of linearity of perception that forms its essential
interest: if one works in a metrics that replicates mechanisms of the human
vision, one can expect that the result of segmentations obtained be relatively
satisfactory, in the sense that it will correspond more to the delimitation that
a human operator could have drawn by hand while seeing the picture.
1.3.5 Distribution of colours of a picture in the different
spaces
In order to place this survey of colorimetric spaces in the context of the
picture process, we have found it interesting to represent a picture in these
different spaces. Naturally, whatever is the space in which the picture
is coded, its aspect must remain the same, but not the distribution of its
colours in the three-dimensional space of colours representation. One
considers the aerial photograph of an urban zone as an example (see Figure
1.3.6). And one gives the representation of the colour clouds that are
present in several classic colorimetric spaces, including those seen previously
(Figure 1.3.7).
This horizontal comparison imposes an observation: if the cloud of points
keeps, with the exception of the orientation, the same aspect in the two
spaces linearly deriving from RGB (KL and XYZ), its geometry in the
two uniforms spaces of the CIE (L*a*b* and L*u*v*) is radically different.
The change of space has consequently a deep modification of the metrics
Figure 1.3.6 Example of colour image used to test various colorimetric spaces,
here displayed in black and white.

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that allow one to anticipate very variable results for the automatic process
applications according to the chosen workspace.
1.3.6 Conclusion
Colorimetry 33
Figure 1.3.7 Distribution of colours of the picture in the different colorimetric
spaces.
It is therefore important not to underestimate problems due to the use of
colour in digital imagery, in particular for photogrammetric processes. At
least one should know how to exploit the passage of a space to one dimension
(the black and white) to a space of at least three dimensions. It is
certain that in a few years there will be for the disposition of users some
spatial images with small pixels of interest to photogrammetrists, and using
more than three spectral bands. Processes used for the black and white
will be reused with multi-spectral pictures, but it will be at the cost of a
considerable loss of information. In fact it will be necessary to start from
zero systematically the analyses of the studied phenomenon to extricate
the best party possible of the available spectral bands. In this optics, one
will need to adopt a colour space with a metrics adapted to the problem

34 Yannick Bergia and Michel Kasser
each time: compression of the image, automatic correlation, automatic
segmentation, automatic shape recognition, etc. Here we presented some
details of trichromatic colorimetry, because it was necessarily very well
studied for the human eye. It is necessary to note therefore that an equivalent
study should be undertaken for a different number of spectral bands,
at each time where the case will happen. . . .
References
Wyszecki G., Stiles W.S. (1982) Colour Science: Concepts Methods and Quantitative
Dated Formulae, second edition, John Wiley & Sons.
Gonzales R.C., Woods R.E. (1993) Digital Picture Processing, Addison-Wesley.
1.4 GEOMETRY OF AERIAL AND SPATIAL PICTURES
Michel Kasser
The usable digital pictures in photogrammetry may originate from three
possible sources: digitized traditional silver halide pictures, digital pictures
originating from matrixes or airborne linear CCD cameras, and the spatial
images of high and very high resolution (between 10 m and 0.8 m pixel
size), these also constituted of CCD matrixes or linear CCD. The geometry
of these different types of pictures is very different, and will be
presented here according to their specificity.
1.4.1 Images with a large field and images with a narrow
field
What distinguishes pictures of spatial origin from those using an airborne
sensor is only the angular field of view, obviously narrower in the case of
the first ones. This field has an influence on several aspects of images, in
particular:
• The direction of observation is pretty much constant in relation to the
solar radiance for the spatial sensors, whereas it varies considerably
in the case of pictures with a large field. Thus we have the evidence
of a phenomenon of brilliant zone, called ‘hot spot’, which is due to
the fact that when the direction of observation comes close to the
direction of the solar radiance, one can no longer observe any zone
of shade whatever the roughness of the ground, or the vegetation, or
the buildings. This direction has a very weak probability to be met in
an image with a narrow field. On the other hand one very often meets
it in aerial pictures with a large field as soon as the sun is high on
the horizon. It materializes a zone of the picture where the reflectance

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Geometry of aerial and spatial pictures 35
of the ground becomes much higher than elsewhere. Another important
point: the direction of reflection of the sun on surfaces of free
water is, for the same reasons of size as for the field of vision of the
sensor, susceptible of provoking a prompt blinding of sensors having
a large field, a situation that is also statistically not frequent on the
spatial high-resolution imaging devices.
• The phenomena of refraction: the light rays captured by a spatial
imager are practically all parallel (the angular field of the Ikonos satellite,
launched in 1999, is 0.9°), and phenomena of differential refraction
between the extreme rays are very weak, otherwise negligible. This
refraction has only very few effects on the absolute pointing of the
sensor in the space, since it leads to a curvature that is significant only
in the last kilometres close to the ground, with therefore a negligible
angular effect since the satellite is between 500 and 800 km away at
least. These aspects are quite different for the airborne imagers with
a large field of view (see §1.1).
• On the other hand, for the phenomena bound to the atmospheric diffusion
(see §1.2), there is no difference between an image obtained from
an airborne sensor flying to an altitude higher than 4 or 5 km and an
image obtained on board a satellite, since in the two cases all the
diffusing layers have been crossed.
• The stereoscopic acquisition on a plane is performed in a very simple
way, essentially because the airplane can acquire any images only when
it flies on a straight axis. According to the requested longitudinal
overlap rate and to the speed of the plane in relation to the ground,
one chooses a rate of image acquisition. And the axis of any image is
in all cases practically vertical. On the other hand, on a satellite one
can get a stereoscopy in several modes, along the track or between
two different orbits. When one works in stereoscopy along the track
(so-called ‘ahead–rear’ stereoscopy, between two similar instruments
pointed ahead and behind, or with an instrument capable of aiming
very quickly in the direction of the orbit), considering the speed of the
satellite on its orbit (of the order of 7 km s 1 ), pictures are nearly
exactly synchronous. In this case the direction of the stereoscopic base
is by necessity that of the track of the satellite, that is imposed by
laws of celestial mechanics and that is virtually impossible to change.
But from several different orbits the satellite can also aim at the same
scene, which provides a ‘lateral’ stereoscopy, and then a considerable
time difference between acquisitions may happen, which sometimes
complicates the work of photogrammetric restitution: for example the
position of the sun is different and therefore shades changed a lot (this
induces difficulties with the automatic correlators), vegetation changed
(new leaves, or loss of leaves as well), cultures are completely different,
levels of water in streams, lakes, or even the sea (tides) are no longer
the same, vehicles have moved, etc. . . . to acquire pictures as quickly

36 Michel Kasser
as possible, satellites are obliged to use the lateral pointing as well as
the ahead–rear stereoscopy, but it is necessary to understand all the
consequences of this for the acquired images when one considers
photogrammetric processes.
1.4.2 Geometry of images in various sensors
There are essentially two main geometries of sensors that are used for
photogrammetric processes: the conical geometry and the cylindro-conic
geometry.
1.4.2.1 Conical geometry: use of films or CCD matrixes
This is well known, since it is the main means of human vision that has
been used since the invention of photography by Nièpce or of the cinema
by the Lumière brothers. It essentially implies a sequential mechanism to
acquire a picture: a very brief exposure time, followed by one technically
necessary dead time to restock a virgin length of film, or to transfer and
to store the digital values corresponding to every pixel on a digital camera.
This dead time is profitably taken on satellites to reorient the aiming system
in order to image as many possible scenes in relation to the plan of work
that is requested.
If the necessary exposure time is too long, there occurs a phenomenon
of linear blurring, because the picture moves continually in the focal plane
with respect to the movement of the airplane or the satellite, which transforms
the picture of a point into a small segment. To overcome this, the
correction of linear blurring (forward motion compensation, or FMC) on
cameras using silver halide films is performed by moving the film during
the exposure time. This film is pushed, indeed, by depression on a very
plane surface (the bottom plate of the camera), and a mechanism moves
this plate in order to follow exactly the movement of the image in the
focal plane during the short period of opening of the shutter. For the CCD
matrixes it is even simpler; it is sufficient to provoke a charge transfer at
the proper speed so that a given set of charges is created by only one
elementary point of the ground: as the picture of this point moves, one
will make the charges created move at the same speed. The FMC, in these
two cases, requires absolute knowledge of the speed vector of the image
in the focal plane, as well as a general mechanical orientation of the sensor
so that its compensation capacity can be parallel to this speed vector. It
is not necessarily easy to know this speed vector in an airplane, since the
leeway of the plane under the lateral wind effect must be known also.
Evidently these parameters of speed may be advantageously provided by
the system of navigation of the plane, currently the GPS. And on a satellite,
these parameters are deduced directly from the orbit and from
coordinates of the target.

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Geometry of aerial and spatial pictures 37
1.4.2.2 Cylindro-conic geometry: use of a linear CCD
This geometry is well known in remote sensing (airborne radiometers,
Landsat satellites . . .), and has been used also in photogrammetry because
of the Spot satellites without discontinuity since 1986. This geometry is
provided naturally by every linear sensor (linear CCD) placed in the focal
plane perpendicularly to the speed vector of the image. It is therefore the
movement of the plane or the satellite that allows one of the dimensions
of the image to be described. The geometric details of these sensors used
in photogrammetry rely especially on the more or less stable speed vector.
In a satellite, the trajectory is locally very precisely a Keplerian orbit,
there is no lack of stability to fear on the parameters of position. On the
other hand the satellite is frequently equipped with solar panels that
are often reoriented automatically thanks to small motors, which create,
in backlash, small changes of attitude. And generally it is impossible to
guarantee a perfect aiming stability during the acquisition of an image,
which results in a small distortion, that may be corrected in the most
advanced means to process the geometry of the images.
But on a plane, the small movements in roll, pitch and yaw are permanent,
with an amplitude and a frequency that depend directly on the
turbulence of air. Therefore inevitably one must perform a permanent record
at least of the attitude, on the three axes, of the sensor. In fact one has also
to measure permanently the three coordinates, as precisely as possible, of
the optic centre of the sensor, using an inertial system and a precise GPS
receiver whose data are quite complementary. Once the data are acquired
one may reconstitute the images as one would have acquired them if the
trajectory of the plane had been perfectly regular. But this correction, in
spite of the efforts performed using excellent inertial platforms, does not
succeed to perfectly correct these movements as soon as there is a little
turbulence, which is very often the case for the urban surveys, generally
done at a low altitude and therefore in a turbulent flight zone. This results
in edges of buildings that are not straight, and finally residual image
distortions that can often cover several pixels. In particular, there may be
real hiatuses of data, owing to the angular movements of the plane being
too rapid, and on another hand geometric aliasing of the picture, a unique
point being imaged on several lines. Such discontinuities are sometimes
impossible to correct by computation, and the only possible resource is then
to ‘fill’ these hiatuses by interpolations between neighbouring strips, but
this is not effectively very satisfactory in terms of picture quality. The only
possibility to avoid such situations consists in installing the sensor on a
servoed platform correcting in real-time movements of the plane, which is
obviously a considerable overcost for the equipment.
In counterpart, this technology permits data coming from several linear
CCD to be combined, with potentially no limit to the number of pixels
measured along a line.

38 Michel Kasser
In this cylindro-conical geometry it is necessary to note a point that is
absolutely fundamental in photogrammetric uses of the acquired images.
Contrary to what occurs in a conical geometry, points are never seen on
several consecutive pictures, since in fact every line of data is geometrically
independent of the previous one. Thus the exact knowledge of the
trajectory is mandatory to be able to put in correspondence the different
successive groups of points seen by the linear CCD. The trajectography is
therefore an essential element of geometry allowing the reconstitution of
the relief, and the images alone are not sufficient to proceed to a photogrammetric
restitution. The only possible validation of these parameters of
trajectory, which become so important here, consists in using effectively
three directions of observation in order to pull a certain redundancy of
determination of the DTM (digital terrain model), that may validate the
whole set of parameters introduced in the calculation. This point is fundamentally
different from the usual geometry with the traditional cameras,
since the stereoscopic basis doesn’t need to be known then (even if we
find an appreciable economical interest in the use of a GPS receiver in the
plane, and even an inertial platform too, in order to get the absolute orientation
of the images, and thus to avoid the determination of ground
reference points, always quite expensive to get; but this equipment is not
mandatory), and that it is in any case redetermined by the calculation
when the model is formed.
Pictures obtained by such devices can be acquired in very long strips,
continuously if need be, which suppresses worries of splices between images
in the longitudinal sense, parallel to the axis of flight. The carving in
successive images is therefore artificial and can be modified by the user
without any problem. Here we should note also that a very strict calibration
of the radiometric response of different pixels is mandatory, as it
is for the linear CCD scanners used to digitize aerial pictures; any failure
to complete it will result in unpleasant linear artefacts. For that reason
the Ikonos satellite has included on board a calibration device regularly
activated, that exposes all pixels to the solar light.
As for the matrix systems, the stereoscopy can be used in the ‘ahead–rear’
mode but also, as for satellites, by using lateral aiming (case of the Spot
satellites). The airborne systems follow the principle of stereoscopy
‘ahead–rear’ and are described in §1.5.2.
The cylindro-conical geometry requires algorithms that are quite different
from those used in classic conical geometry for photogrammetric restitution.
These algorithms have been explored extensively for the restitution
of the Spot images since the 1980s. Nevertheless, they remain poorly known
and forbid de facto the use of equipment and software not designed for
this geometry, which thus prevents the use of these data on other stereoplotting
devices.

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1.4.3 Conclusion
Digital image acquisition 39
The different geometries used to acquire pictures have some important
consequences when a photogrammetric process is to be performed. It is
often not just a detail, since if one doesn’t take the necessary precautions
one may find it impossible to validate by internal means the results
obtained. Much attention must be paid to the practical consequences of
choices of images, in particular with the arrival on the market of very high
spatial resolution images, apparently very similar to the aerial pictures,
but which have completely different geometric properties.
In the domain of the large field airborne imagery, linear CCDs systems
seem especially destined to provide very high resolution pictures, but whose
metrics is not very critical (devoted to photo-interpretation, for example).
On the other hand the matrix systems, providing an extremely rigorous
geometry, will be much more suitable to photogrammetric uses.
1.5 DIGITAL IMAGE ACQUISITION WITH AIRBORNE
CCD CAMERAS
Michel Kasser
1.5.1 Introduction
Currently most processes of photogrammetry turn toward a larger and
larger use of digital images. Considering the reliability and the quality of
materials for aerial image acquisition used several decades ago, but also
considering the excellent knowledge that we have about the defects of this
chain of image acquisition, research laboratories and constructors wisely
started with the reuse of previous achievements. They proposed therefore
first to digitize images obtained in aerial image acquisitions on argentic
traditional film. Nevertheless, this solution is only a temporary solution,
and as we will see in §1.8, the digitization of films is a delicate and costly
operation, which brings its own share of deterioration to images. It is
therefore natural that studies have been led, initially, since 1980, at the
DLR in Germany for the Martian exploration, then in France since 1990,
to get digital images directly in the airplane itself. Studies moved in two
simultaneous directions, using two CCD devices: linear CCD, according
to the model of sensor popularized by the spatial imagers like SPOT or
Ikonos, using the advancement of the plane to scan one direction of the
image, and matrixes, that are the modern and conceptually simple copies
of traditional photography.
These two directions of research first gave rise to realizations of laboratories
(e.g. HRSC sensor using several linear CCDs of the DLR, matrix
cameras of the IGN-F), then to industrial realizations (ADS 40 of LH
Systems in 2000 and MDC of Zeiss Intergraph in 2001). Studies have

Figure 1.5.1 (a) The digital modular camera DMC 2001 from Zeiss-Intergraph.
Figure 1.5.1 (b) Three digital cameras from IGN-F: (from left to right) with one
(1995), with two and with three separate cameras (2000), using
KAF 6300 (2k × 3k pixels) or KAF 16800 (4k × 4k), or KAF
16801 (4k × 4k with antiblooming) chips from Kodak.
Figure 1.5.1 (c) The ADS-40 digital camera from Leica-Helava (left), the CCD
lines observing various wavelengths (centre) and the optical
subsystem for the separation of the visible light into 3 colours
RGB (right).

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shown quite clearly fields of interest of these two techniques, as well as
their limitations. They have also shown how much the community of
photogrammetrists had difficulties imagining the future with tools very
different from older ones: this community is ready to replace one link of
the photogrammetric chain at a time, but not much more, which is easily
comprehensible. Photogrammetrists have, for example, clearly shown their
concern, not because of directly digital images, but because of the entirely
new situations where their empirical ability would have to be reconstituted
from zero, in particular being entirely at the mercy of software
editors. For example, linear CCD systems give a quite different geometry
to process the images as compared to traditional techniques.
The digital cameras developed according to these two general types are
presented briefly below. They have in common the use of the CCD, which
offers an extraordinary luminous response linearity compared with the
usual argentic processes: these are really radiometers, perfectly calibratable,
that make a much easier job, for example at the radiometric
connections between neighbouring images at the time of the realization of
mosaics or orthophotographies. The advantage of this linearity is also very
clear when one has to suppress by digital processes the atmospheric
diffusing fog: this operation is extremely simple and efficient with the CCD
sensors, whereas it is impossible to automate it on argentic colour images.
Currently the two solutions (linear CCD and matrixes) seem to have
slightly different domains of applications, and as we already evoked it in
§1.4, linear CCD systems are preferably destined to provide images of very
high resolution but whose metrics is not very critical (for the merely visual
exploitation and without precise measurements, for example, which represents
a very large part of the market of aerial imagery). On the other hand
the matrix systems, providing an extremely rigorous geometry (and even
much better than that of argentic pictures, digitized or not), are far more
suited to photogrammetric uses. But only after several years of market
reaction to these offers can we make valid conclusions, and it is not possible
for the authors to push the analysis farther at the time of writing this
book. Some elements already presented in §1.4 will not be repeated here,
and we refer the reader back to this section if necessary.
1.5.2 CCD sensors in line
Digital image acquisition 41
It was in order to prepare a mission to Mars, that finally didn’t fly, that
the DLR (Germany) studied in detail the HRSC tool (high resolution stereo
camera). This tool, which was conceived for the spatial applications, was
then tried with success on airborne missions. It has been used industrially
since 1999 in production within the Istar company (France), and the new
camera ADS 40 of LH Systems is based on the same concepts.
The principle is as follows: in the focal plane of high-quality optics is
installed a set of linear CCDs, which allows at any given instant the ground

42 Michel Kasser
to be imaged in several directions. The prototype of the ADS 40 (Fricker,
et al. 1999) uses four linear CCD or groups of linear CCD of 12,000
elements each, one that gets images to the vertical of the plane, with the
others imaging following a fixed angle with respect to the vertical (several
angles are possible, according to the uses) toward the front and the rear
of the plane. Thus, a point of the ground is seen successively under three
different angles, which quite obviously permits one stereoscopic reconstitution
of the relief. Some of these sensors work in panchromatic mode,
others are equipped with spectral filters. Some linear CCD used in panchromatic
mode are formed of two staggered linear CCD, separated by half a
pixel, which may allow one to rebuild the equivalent of the signal provided
by a linear CCD of 24,000 pixels. One then has a resolution that is without
any comparison with any other airborne sensor used, even though the
geometric quality of such images allows some minor distortions.
Considering the trajectory of the plane, that is evidently uncertain and
subject to unforeseeable and important movements, it is necessary to know
at any instant and with a very high precision the real position of sensors in
the space. This problem, which does not appear on a satellite (whose
trajectory is extremely steady), implies for a plane the use of powerful additional
systems capable of correcting at different times the effects of movements
of the plane on the recorded image, that would be completely
unusable without it. For that purpose, one attaches to the system an inertial
platform as well as a GPS sensor; the fusion of the output data of these two
sources is made exploiting a Kalman filter. Let us note that the coupling
inertial platform GPS doesn’t necessarily permit one to determine in a
satisfactory way the yaw movements of the plane: it would be determined
correctly by the Kalman filter only if the plane did not remain for a long
time right in line, which is unfortunately unavoidable. And long-distance
systematisms of the GPS (for example, if it is used in trajectography mode),
are directly transferred as deformations of the survey performed. Besides,
one should not overestimate the operational performances of the GPS, and
very short losses of signal can occur in flight, which leads at the time of the
treatment to short interruptions of the corrections provided by the inertial
platform: it almost produces automatically a set of irretrievable distortions
of the image acquired. Therefore it is not foreseeable to get a geometric
precision, expressed in pixels, comparable with what the digital images
usually provide with matrix imagers in conical perspective. Typically one
can count, in equivalent cases, on residual errors of several pixels for images
obtained with linear CCD sensors, against 0.1 pixels on matrix images.
The results published in 2000 show that the pros and cons of this sensor
type ADS 40 include typically:
• The possibility of an image with a number of distinct points on the
ground close or even superior to what is available in aerial digitized
pictures (12,000 pixels are roughly equivalent of what provides an

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aerial picture 24 × 24 cm digitized with 20 m of pixel, and 24,000
is achievable if necessary).
• The geometric distortions due to inertial system insufficiencies are
weak, but remain generally visible (some pixels): the metrics of the
image therefore shows some small defects.
• The dynamics of the image is satisfactory, but the necessity to transfer
charges in the linear CCD to a very high speed implies a very limited
exposure time, which does not allow dynamics as high as that on
matrixes to be reached. Images, nevertheless, offer an excellent linearity
of response.
• The geometry of images (cylindro-conic perspective) implies new modes
of digital data processes, which seem quite suited to the automated
determination of digital surfaces models (DSM), but forbid the use of
standard softwares of classic photogrammetry stations.
• The restitution of the colour is obtained by adding in the focal plane
additional linear CCDs equipped with filters. For example, the linear
CCD that images along the vertical is in fact replaced by three parallel
and very close linear CCDs equipped with the three usual filters, RGB.
Other linear CCDs can be equipped with other filters, e.g. for the infrared.
But if the three colours are obtained through lines that do not
observe exactly the same area simultaneously, some artefacts appear on
mobile objects, of course, but also when strong perspective differences
are present in the image (high buildings, for example).
1.5.3 Matrix CCD sensors
Digital image acquisition 43
The principle consists in preserving the usual geometry of the classic image
acquisition (conical perspective), and using a CCD matrix as large as
possible in the focal plane of the optics. Studies performed at IGN-F from
the beginning of the 1990s (Thom and Souchon, 1999) show how such
images could be inserted in photogrammetric classic chains, and what were
the limitations and advantages of such matrix cameras:
• The CCD matrixes are perfectly suitable for the compensation of linear
blurring due to the speed (forward motion compensation or FMC), and
even with more simplicity than on traditional FMC airborne cameras
since it is performed electronically, without any mechanical movement.
This allows a long exposure duration (several tens of milliseconds if
need be), compatible with a very weak lighting (wintry or dusky image
acquisitions) while preserving an excellent signal/noise ratio.
• The sensitivity of the CCD, added to the possibility of using long exposure
times, is the origin of a dynamics of the image that can reach
considerable values, a digitization on 12 bits being hardly sufficient.
It is quite different from silver halide film image performances that,
even if digitized in the best conditions, would hardly deserve 6 bits.

44 Michel Kasser
It is an essential asset, for example, for removing easily the atmospheric
fog in post-process, or for observing in a satisfactory way shades
and in the very luminous zones as well. It is also an essential asset for
tools of automatic image matching, since with such a dynamic one no
longer finds any uniform surface, and numerous details with quite faint
differences of radiometry remain discernible.
• The largest commercially available matrixes in 2000 have dimensions
of the order of 7,000 × 9,000 pixels. This represents a more modest
pixel number than that of a digitized silver halide image. Nevertheless,
cases of the use of such images of very high dynamics have been valued
on applications of current middle-scale cartography: an equivalent
service to a given ground size of pixel on a digitized argentic image
is more or less provided by a two times larger pixel on a digital image
of very large dynamics. Compared to the service provided by a traditional
digitized image, it corresponds, therefore, to a digital image
about half as large. Let us note that with the remarkable performances
of these images it would be quite acceptable and logical to
interpolate pixels of dimension half as large, which would so give
the equivalent of an image 8,000 × 8,000 from a matrix 4,000 ×
4,000. One would thus get the content of an image quite similar to a
digitized argentic one, although of incomparably better linear radiometry.
Nevertheless, for a given site of study this may imply, according
to the chosen matrix size, more axes of flight than for a classic image
acquisition, which is a source of additional costs. Developments of
large dimension matrixes, by chance, follow the considerable demand
for digital pictures for the general public, so that they evolve rapidly.
Apparently formats used by amateurs (24 × 36 mm) and professionals
(60 × 60 mm) are currently well covered by matrixes of 2,000 × 3,000
and 4,000 × 4,000. The likely evolutions could go circa a strong reduction
of costs, the trichromy, and maybe an increase of current matrix
sizes, but not necessarily very important (rather for the professional
photographers, who represent a small section of the market) knowing
that the data storage is no longer a limitation for these markets due
to the availability of large data storage capabilities. The way chosen
by the ZI society (DMC camera) consists in a combination of various
modular matrix subsets based on matrixes about 4,000 × 7,000,
capable of reconstituting 8,000 × 14,000 images, with the possibility
of supplementary matrixes equipped with filters capable of reconstituting
of colours. The elementary matrixes are equipped with individual
optics aiming to divergent axes and assuring a small overlap between
each of the four images. The resulting geometry is equivalent, within
an accuracy of about 0.1 pixels, to an image acquired in only one
block, by one optic.
• The restitution of the colour can be obtained of two ways: either on
certain matrixes a set of filters is deposited on the pixels, or one uses

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Digital image acquisition 45
three matrixes equipped separately with filters. The first solution
induces delicate problems of reconstitution of the colour, and requires
well-developed software to let only small artefacts (e.g. on borders, or
on very local details displayed on only one pixel). It implies either a
subset of 4 pixels (e.g. Kodak: two with green, one with blue and one
with red filters), or a different arrangement of the matrix, where the
lines are staggered from a half-pixel, and the 3 filters are regularly
spaced on a 3-pixel subset (e.g. Fuji: on each line the filters are R G
B R G B . . ., for example the R being staggered by 1.5 pixels from
a line to the other), a solution that provides a better colour synthesis.
The second solution is costlier, because it finally results in the equivalent
of three complete cameras regrouped together, but it permits the
perfect reconstitution of colours in all circumstances.
• The metrics of the image is absolutely excellent, and even significantly
superior to the accessible metrics on classic film cameras. Even if the
latter are nearly perfect in terms of distortion, the film represents a
medium whose distortions are far from negligible. These distortions
are due to treatments at the time of the development and the drying,
that stretch the film in an anisotropic way. They are also, and this
phenomenon is not so well known (see §1.1), due to dust on the
bottom plate of the camera that prevents a good contact of the film
on the table to depression, and creates some significant bumps at the
time of the image acquisition. It provokes local distortions of the image
that are pure artefacts, nearly impossible to model. In the digital matrix
cameras, the calibration is performed as for a classic camera, but as
the sensor is monolithic, no distortion can now occur, and one observes
a precision in geometric computations that is generally better that 0.1
pixels.
• The available optics offers a much wider choice for amateur cameras
than for the classic aerial cameras. Practically all optics adapted to the
60 × 60 format (professional photography) are satisfactory, and this
at obviously much more modest costs. Indeed the classic defects of
optics, distortion, vignetting, etc., can be corrected by a posteriori
calculation, and only the resolution of the optics and its dimensional
stability in the time remain important parameters.
1.5.4 Specifications of digital aerial image acquisitions
The use of airborne digital cameras induces significant changes in terms
of specification of image acquisitions. Notions of height of flight and
size of pixel can be considered as largely independent, in particular due
to the much larger choice of available optics. Even the notion of scale
disappears completely, with all the empirical knowledge that is attached
to it. The maximal angle of field of the image will be chosen according
to the acceptable hidden parts and the need of precision on an altimetry

46 Michel Kasser
restitution, expressed in particular through the B/H ratio of the distance
between successive positions of the camera at the time of two successive
image acquisitions, divided by the altitude of flight. The size of pixel will
be chosen according to the size and the nature of objects to survey and
to detect, and to the dynamics of the accessible image with the considered
camera. It is with these two parameters that one will determine the project
of flight, and in particular the altitude.
One will note some empirical rules that will be detailed in §1.9: the precision
of pointing of an object is performed in general to better than 0.3
pixels, and to identify an object easily it is desirable that it is not smaller
than 3 × 3 pixels. This allows one to specify the really necessary pixel sizes.
For example, with a matrix camera with a very large dynamics, to achieve
an orthophotography on an urban zone where a DTM is already available,
one will choose a long focal distance to limit the hidden parts of buildings,
and the raw size of pixel will be chosen, e.g. as 50 cm to have a satisfactory
description of buildings, or of 30 cm if one wants to have a tool
of management of urban furniture. These sizes of pixels will be reduced if
the dynamics of the image is low (respectively 30 cm and 15 cm for a digitized
classical image).
In a traditional image acquisition the height of flight also intervenes by
the atmospheric fog, more or less acceptable, that will result: sometimes,
to get a very weak fog with a height superior to 4,000 m may prove to
be an impossible mission under certain latitudes in classic photography.
In digital imagery, if the dynamics is sufficient it allows the removal of
the atmospheric fog while preserving a good quality of colour and a good
capacity to work in zones of shades. It permits a considerable reduction
in the delays bound to the meteorological risks, but also eases the constraint
on the parameter of flight height, if need be.
References
Fricker P., Sandau R., Walker S. (1999) Digital Aerial Sensors: possibilities and
problems, Proceedings of OEEPE Workshop on Automation in Digital
Photogrammetric Production, Marne-la-Vallée, 22–24 June, Public. OEEPE no.
37, pp. 81–90.
Thom C., Souchon J.-P. (1999) The IGN Digital Camera System, Proceedings of
OEEPE Workshop on Automation in Digital Photogrammetric Production,
Marne-La-Vallée, 22–24 June, Public. OEEPE no. 37, pp. 91–96.

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1.6 RADAR IMAGES IN PHOTOGRAMMETRY
Laurent Polidori
1.6.1 Overview
Images obtained from a synthetic aperture radar (SAR) are very sensitive
to terrain undulations, and this sensitivity has been the basis for the development
of several relief-mapping techniques using one or several radar
images, namely, radargrammetry, interferometry and radarclinometry
(Polidori, 1991). Each of these techniques was initially proposed more than
25 years ago, and their theoretical bases were established in the 1980s. The
state-of-the-art of radar mapping has been presented in detail by Leberl
(Leberl, 1990), based on airborne campaigns and on pioneering spaceborne
SARs like SEASAT (1978), SIR-A (1981) and SIR-B (1984), but the actual
potential of radar techniques has been known only for a few years, due to
the lack of SAR data before the 1990s. The launch of several spaceborne
SARs in recent years (ERS, JER-S, RADARSAT, SIR-C) has led to further
experiments and to a better estimation of the accuracy of radar-derived
DSMs (digital surface models).
Several specific properties of radar sensors must be mentioned to explain
their potential for mapping.
An active device
A radar sensor in general, and a synthetic aperture radar in particular,
provides its own power through a transmitting antenna: this contributes
to making radar a so-called ‘all-weather’ sensor by allowing acquisitions
even at night. Moreover, since day and night acquisitions correspond to
ascending and descending orbits, this also contributes to opposite side
viewing capabilities so that hidden areas are greatly reduced.
Absolute location accuracy
Radar images in photogrammetry 47
Attitude (i.e. roll, yaw and pitch angles), which in the case of optical
images is the major contributor of absolute location error, has no effect
on location in a SAR image. Indeed, the computation of image point location
in a SAR image requires only a slant range and a Doppler frequency
shift, and these magnitudes do not depend on sensor attitude.
Sensitivity to relief
Radar image location is based on slant range measurements between
the antenna and each terrain target: this is why terrain elevation has a
direct effect on image location. This effect can be locally described as

48 Laurent Polidori
a proportional relationship between a height variation z and a slant range
variation R for a given incidence angle :
R z
cos ,
where is the angle between the local vertical and the viewing direction.
At pixel scale, R is a parallax that can be measured to derive an
elevation: this is the basis for radargrammetry. At wavelength scale, R
can be estimated from a phase shift between two echoes: this is the basis
for interferometry. Apart from this geometrical sensitivity, a radiometric
sensitivity can be mentioned, since terrain orientation has an impact on
radar return intensity: this is the basis for radarclinometry (or radar shape
from shading).
Coherence
Radar signals are coherent, which means that they are determined in terms
of amplitude and phase. The generation of a SAR image would not be
possible otherwise. This characteristic makes radar sensors very sensitive
to relief because of interferometric capabilities.
Atmospheric effects
The effects of the atmosphere and in particular the troposphere can be
neglected at pixel scale, i.e. a radar image can be acquired and accurately
located whatever the meteorological conditions. On the contrary, these
effects cannot be neglected at wavelength scale, and they produce artefacts
in interferometric products. For instance, a radar echo acquired under
heavy rain conditions may have a phase delay of several times 2 even if
the scene geometry has not changed.
1.6.2 Radargrammetry
Radargrammetry is an adaptation of the photogrammetric principles to
the case of radar images. Indeed, it is based on parallax measurements
between two images acquired from different viewpoints. However, radargrammetry
cannot be carried out directly with photogrammetric tools, for
two main reasons.
First, the SAR geometry is modelled by specific equations: this implies
that analogue stereo plotters are not suitable, and that the first rigorous
implementations could only be achieved with analytical plotters (Raggam
and Leberl, 1984).
The second reason is that stereo viewing is difficult and uncomfortable
with radar images, in particular in the case of rugged terrain. This is due

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to the fact that bright points and shadows suffer migration from one image
to another due to the difference in illumination. However, stereo viewing
capabilities can be acquired with practice, as relief perception is basically
a psychological process (Toutin, 1997a).
The feasibility of radargrammetry was demonstrated for airborne radar
data (Leberl et al., 1987) as well as for spaceborne radar data (Leberl
et al., 1986). According to experiments made over different landscapes, it
is now well known that this technique can provide 3D measurement with
an accuracy of a few pixels, i.e. around 20 m with airborne SAR (Toutin,
1997b) and between 20 and 50 m with ERS (Toutin, 1996; Raggam et al.,
1993) or RADARSAT (Sylvander et al., 1997; Marinelli et al., 1997). As
expected, the radargrammetric error tends to increase in case of steep relief.
1.6.3 Interferometry
Radar images in photogrammetry 49
SAR interferometry consists in deriving terrain elevation from the phase
difference between two radar echoes acquired from very close antenna
positions (Zebker and Goldstein, 1986; Massonnet and Rabaute, 1993).
The two images can be obtained either from two antennas constrained to
remain on parallel paths (this is generally the case for airborne systems)
or from the same antenna during two passes. If these images are properly
registered, the phase difference can be computed for every pixel and stored
in an interferogram. Although the phase difference has a simple relationship
with the slant range difference and therefore with elevation, relief
cannot be derived so easily due to two severe limitations.
The first limitation is the dependence of radar phase on non-topographic
factors, such as atmospheric variations (Goldstein, 1995; Kenyi and
Raggam, 1996), land cover changes or sensor miscalibration (Massonnet
and Vadon, 1995): these contributions to phase shift contaminate the interferogram
and can be converted to elevation, contributing to the error of
the output digital surface model. This is generally the case when the time
interval between the acquisitions is too long, so that important changes
have occured not only in the atmospheric refraction index but also in the
surface roughness or electromagnetic properties.
The second limitation is the fact that the radar phase is not known in
absolute terms but only modulo 2, so that interferograms generally exhibit
fringes that must be unwrapped.
The performance of phase unwrapping mainly depends of the B/H ratio,
i.e. the ratio between the stereoscopic baseline and the flight height:
• when B/H is smaller, the fringes are wider: it becomes easier to unwrap
them, but a given height gradient has less impact on the radar phase,
which means that the interferogram is less sensitive to relief;
• when B/H is larger, the fringes become narrow and noisy: they are
too sensitive to relief and they are more difficult to unwrap.

50 Laurent Polidori
In the most usual configuration, interferometric images are acquired with
a single antenna at different dates. The problem then is that the baseline
cannot be predicted. Therefore, the accuracy of the method, which can be
determined a posteriori, cannot be predicted before the acquisitions.
The most accurate results, which are close to the theoretical limits, are
generally obtained with simultaneous dual antenna acquisitions. Interferometric
processing based on the airborne TOPSAR system (Zebker et al.,
1992) provided accuracies around 1 m in flat areas and 3 m in hilly
areas (Madsen et al., 1995), and the CCRS dual-antenna SAR system
provided a 10 m accuracy in mountainous and glacial areas (Mattar
et al., 1994).
Single-antenna interferometry provides very heterogeneous results, due
to the double influence of the spatial baseline (which cannot be predicted)
and the time interval (which is generally too long) (Vachon et al., 1995).
These influences vary according to landscape characteristics, and the accuracy
depends on slope and land cover. Since these characteristics are often
heterogeneous over 100 km side scenes, evaluating an interferometric accuracy
over such a huge area is not very meaningful. Under suitable conditions
(moderate relief, short time between acquisitions, no atmospheric variations),
the error of interferometric products may be as small as 5 m with
ERS data (Dupont et al., 1997) and 7 m with RADARSAT data (Mattar
et al., 1998). As soon as ideal conditions are not fulfilled, errors often
increase to several tens of metres.
During the generation of a radar interferogram, an associated product
called the coherence image is usually computed as well, in order to display
the correlation between the two complex echoes. This product provides
useful information on the interferometric accuracy, because phase noise
increases the output height error proportionally. However, correlation is
also a very interesting thematic product, since correlation is an indicator
of surface stability. For instance, rocky landscape and urban structures are
very stable, so that they are generally mapped with high interferometric
correlation, while forested areas and, above all, water, have very low correlation
because the surface geometry within each pixel has permanent
changes comparable to the wavelength (Zebker and Villasenor, 1992).
1.6.4 Radarclinometry (shape from shading)
While radargrammetry and interferometry are based on the principle of
stereoscopy, and therefore on the geometry of the radar images, radarclinometry
makes use of image intensity and can provide a DSM using a
single radar image.
Radarclinometry is a particular case of shape from shading, insofar as
it determines the absolute orientation of each terrain facet using its intensity
in the radar image. In fact, this technique is a quantitative application
of the visual perception of relief one has looking at a radar image.

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The link between terrain orientation and radar image intensity is
described by a backscattering model, in which the intensity is expressed
as a function of the incidence angle (between the viewing direction and
the perpendicular to the terrain surface) and the backscattering coefficient
(similar to reflectance for optical imagery). Radarclinometry is basically
an inversion of such a model. However, inverting a backscattering model
is constrained by two major limitations:
• image intensity depends not only on the incidence angle but also on the
backscattering coefficient and therefore on ground characteristics (land
cover, roughness, moisture . . .) which in most cases are not known;
• one particular value of the incidence angle corresponds to an infinity
of possible terrain orientations, because surface azimuth or aspect also
contributes to the incidence angle.
Due to these ambiguities, any radarclinometric algorithm must inject
external constraints or hypotheses in order to make the inversion possible.
To mention the most classical hypotheses, the first ambiguity is generally
solved by assuming a homogeneous land cover (which implies that intensity
variations are caused by slope variations only) and the second one by
neglecting the slope component oriented along the track. A number of
algorithms have been proposed to overcome these difficulties (Frankot
and Chellapa, 1987; Thomas et al., 1989; Guindon, 1990; Paquerault and
Maître, 1997).
Guindon (1990) obtained an elevation above 200 m from SEASAT data
(with around 20°, i.e. a very deep incidence) over a mountainous area
with steep slope: these are the worst conditions for radarclinometry. On
the contrary, Paquerault and Maître (1997) obtained an error of the order
of 20 m using RADARSAT over French Guyana, where the landscape is
uniformly forested with gentle hills: this corresponds to ideal conditions
for radarclinometry.
Finally, it should be noted that the elevation error is not very meaningful
to evaluate the performance of radarclinometry, which is bascally
a slope-mapping technique. The fact that standard elevation error is often
used as a unique quality criterion for DSMs implies that very smooth
surfaces are generally preferred, while radarclinometry is very sensitive to
microrelief.
References
Radar images in photogrammetry 51
Dupont S., Nonin P., Renouard L. (1997) Production de MNT par interférométrie
et radargrammétrie. Bull. SFPT, no. 148, pp. 97–104.
Frankot R., Chellapa R. (1987) Application of a shape-from-shading technique to
synthetic aperture radar. Proceedings IGARSS ’97 (Ann Arbor), pp. 1323–
1329.

52 Laurent Polidori
Goldstein R. (1995) Atmospheric limitations to repeat-pass interferometry. Geophysical
Research Letters, vol. 22, no. 18, pp. 2517–2520.
Guindon B. (1990) Development of a shape-from-shading technique for the extraction
of topographic models from individual spaceborne SAR images. IEEE
Transaction on Geoscience and Remote Sensing, vol. 28, no. 4, pp. 654–661.
Kenyi L., Raggam H. (1996) Atmospheric induced errors in interferometric DEM
generation. Proceedings of IGARSS ’96 Symposium (Lincoln), pp. 353–355.
Leberl F. (1990) Radargrammetric image processing. Artech House, Norwood,
p. 613.
Leberl F., Domik G., Raggam H., Kobrick M. (1986) Radar stereomapping techniques
and application to SIR-B images of Mt. Shasta. IEEE Transaction on
Geoscience and Remote Sensing, vol. GE-24, no. 4, pp. 473–481.
Leberl F., Domik G., Mercer B. (1987) Methods and accuracy of operational digital
image mapping with aircraft SAR. Proceedings of the Annual Convention of
ASPRS, vol. 4, pp. 148–158.
Madsen S., Martin J., Zebker H. (1995) Analysis and evaluation of the NASA/
JPL TOPSAR across-track interferometric SAR system. IEEE Transactions on
Geoscience and Remote Sensing, vol. 33, no. 2, pp. 383–391.
Marinelli L., Toutin T., Dowman I. (1997) Génération de MNT par radargrammétrie.
Bull. SFPT, no. 148, pp. 89–96.
Massonnet D., Rabaute T. (1993) Radar interferometry: limits and potential. IEEE
Transaction on Geoscience and Remote Sensing, vol. 31, no. 2, pp. 455–464.
Massonnet D., Vadon H. (1995) ERS-1 internal clock drift measured by interferometry.
IEEE Transaction on Geoscience and Remote Sensing, vol. 33, no. 2,
pp. 401–408.
Mattar K., Gray L., Van der Kooij M., Farris-Manning P. (1994) Airborne interferometric
SAR results from mountainous and glacial terrain. Proceedings
IGARSS’94 Symposium (Pasadena), pp. 2388–2390.
Mattar K., Gray L., Geudtner D., Vachon P. (1998) Interferometry for DEM and
terrain displacement: effects of inhomogeneous propagation Canadian Journal
of Remote Sensing, vol. 25, no. 1, pp. 60–69.
Paquerault S., Maître H. (1997) La radarclinométrie. Bull. SFPT, no. 148, pp. 20–29.
Polidori L. (1991) Digital terrain models from radar images: a review. Proceedings
of the International Symposium on Radars and Lidars in Earth and Planetary
Sciences (Cannes), pp. 141–146.
Raggam H., Leberl F. (1984) SMART – a program for radar stereo mapping on
the Kern DSR-1. Proceedings of the Annual Convention of ASPRS, pp. 765–773.
Raggam H., Almer A., Hummelbrunner W., Strobl D. (1993) Investigation of the
stereoscopic potential of ERS-1 SAR data. Proceedings of the 4th International
Workshop on Image Rectification of Spaceborne Synthetic Aperture Radar
(Loipersdorf, May) pp. 81–87.
Sylvander S., Cousson D., Gigord P. (1997) Etude des performances géométriques
des images RADARSAT. Bull. SFPT, no. 148, pp. 57–65.
Thomas J., Kober W., Leberl F. (1989) Multiple-image SAR shape from shading.
Proceedings IGARSS ’89 (Vancouver, July), pp. 592–596.
Toutin Th. (1997a) Depth perception with remote sensing data. Proceedings of
the 17th Earsel Symposium on Future Trends in Remote Sensing (Lyngby, June)
pp. 401–409.

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Toutin Th. (1997b) Accuracy assessment of stereo-extracted data from airborne
SAR images. International Journal for Remote Sensing, vol. 18, no. 18, pp.
3693–3707.
Vachon P., Geudtner D., Gray L., Touzi R. (1995) ERS-1 synthetic aperture radar
repeat-pass interferometry studies: implications for RADARSAT. Journal Canadien
de Télédétection, vol. 21, no. 4, pp. 441–454.
Zebker H., Goldstein R. (1986) Topographic mapping from interferometric SAR
observations. Journal of Geophysical Research, vol. 91, no. B5, pp. 4993–4999.
Zebker H., Villasenor J. (1992) Decorrelation in interferometric radar echoes. IEEE
Transaction on Geoscience and Remote Sensing, vol. 30, no. 5, pp. 950–959.
Zebker H., Madsen S., Martin J., Wheeler K., Miller T., Lou Y., Alberti G.,
Vetrella S., Cucci A. (1992) The TOPSAR interferometric radar topographic
mapping instrument. IEEE Transaction on Geoscience and Remote Sensing,
vol. 30, no. 5, pp. 933–940.
1.7 USE OF AIRBORNE LASER RANGING SYSTEMS FOR
THE DETERMINATION OF DSM
Michel Kasser
Airborne laser ranging systems for DSM 53
1.7.1 Technologies used, performances
Airborne laser telemetry (ALRS, an acronym that stands for airborne laser
ranging system) is the normal term used in the 1970s for the airborne
profile recorders (APR) that provided, in a continuous way, a very precise
vertical distance from the airplane to the ground (for example Geodolite®
of Spectra-Physics); the positioning of the plane was obtained then by
photographic means that were not very precise in planimetry, the altimetric
reference being directly the isobar surface at the level of the plane.
These processes, fallen into obsolescence since the beginning of the 1980s
because of insufficient precision of positioning, regained an interest when
the GPS appeared as a very precise localization system, with data being
processed after the flight. A large variety of equipment is available in 2000,
including the laser rangefinder, its scanning device, an inertial platform
and a GPS receiver, and of course the originality of every equipment resides
in the proposed software packages.
The principle of functioning is as follows:
• The ALRS provides in a continuous way, at rates from 2 to 100 kHz,
the time of propagation of a laser impulse given out by a powerful
laser diode working in the near IR. This laser rangefinder is fixed to
the plane as rigidly as possible. It may, in general, according to requirements,
provide some different distances, for example that on the first

54 Michel Kasser
received echo (to measure objects over the ground, like an electric
power line), or on the contrary on the last (to measure ground under
vegetation), or again all echoes received for each shot (but then the
quantity of data greatly increases). The precision of the rangefinder is
in the order of some centimetres in the absolute, but in fact what
matters is the interaction of the laser beam with the object targets,
which is geometrically not very definite in most cases (e.g. high vegetation,
building borders . . .). The beam is slightly diverging (typically
1 mrad), and even though the plane cannot fly high, considering the
weak optic signal that is allowed not to create any ocular hazards, the
analysis spot therefore has a diameter of several decimetres. A variant
of this technology must be mentioned; it uses a continuous laser source
modulated by a set of frequencies permitting ambiguity resolution (on
the model of the old Geodolite® already quoted), but it is not widely
used.
• An optico-mechanical scanner device allows the laser beam to be sent
sequentially in different directions, which permits, with the advancement
of the plane a scan of the ground, in a strip around the ground
trace to be performed.
• In order to know the position of every laser shot in the space in spite
of the unknown movements of the plane, the ALRS is coupled rigidly
to an inertial unit platform. It provides information at a rate compatible
with the movements of the plane, typically from 200 to 500 Hz.
It must be initialized (some minutes or tens of minutes), so that its
core components are in a stationary thermal regime. Its data errors
are characterized by a bias proportional to the square of the time,
which implies very frequent corrections.
• In order to correct the inertial unit that would drift quickly to excessive
values without such external help, a precise GPS receiver is added
to the whole. This receptor provides, in differential mode, the positions
of its antenna as often as possible, generally between rates of 1 and
10 Hz, and the post-processing must provide precision compatible with
the requirements of the study, which in turn implies naturally the localization
of the reference GPS receiver in relation to the surveyed area.
• To complement this equipment, there is a PC unit to pre-process data
and store the large quantities of observed data, to help with the navigation,
etc.
The post-processing of measures is an intense operation. The GPS calculation,
then the fusion of the GPS with inertial data, is an operation that
may be automated to a large extent. Then it is necessary to process echoes,
that is to say to filter non-applicable echoes, and this operation is not
currently automated at all. For example to get a DTM under trees, it is
necessary to identify ‘by hand’ which echoes probably come from the

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ground and which do not. Considering the number of echoes to treat,
this operation, even with the help of the software, is very tedious. The
impersonal and systematic character of the target selection (whatever the
target, there is always an echo) is one of the fundamental features of
this survey mode, and it may imply heavy data post-processing in certain
configurations.
1.7.2 Comparisons with photogrammetry
Airborne laser ranging systems for DSM 55
Surveys by ALRS are significantly different from photogrammetric surveys,
either using traditional digitized images or direct digital imagery.
These surveys are in a semi-experimental period, in which the distributed
and published information are not necessarily all applicable considering
the commercial implications. ALRS surveys have therefore a
low maturity compared to photogrammetry. One is nevertheless able to
identify common features and weaknesses of these two techniques. An
excellent survey on this topic is that by Baltsavias (1999), from which
we take here certain elements. The main comparison between ALRS and
photogrammetric surveys must include types of data process that are at a
semi-experimental level in the two domains, which includes therefore, for
example, developments in progress concerning automatic image matching
and multi-stereoscopy.
Points that we will keep in this comparison are as follows:
• The DTM issued from ALRS can be available, if the type of work is
suitable, in a very short time after the flight. For example, for the
linear sites surveys without vegetation (urban surveys, power lines),
the post process can be entirely automated, and the geometric data
supplied in one or two hours. To the contrary, the supplying of DTM
by automatic image matching requires processes that are not yet
completely automatic, and are always quite long.
• The equipment used in ALRS is sophisticated and expensive, and some
unit components may experience some export limitations according to
their countries of origin (USA for example). The maintenance when
in use is therefore still not very easy. We are in the presence of technologies
of which some are very recent, evidently in contrast with
photogrammetry where devices of aerial image acquisition are industrialized
at a very high level, and are of a remarkable reliability.
• The installation of the ALRS equipment on board a photogrammetric
plane or a helicopter is a delicate phase that requires, for example,
aiming toward the ground, which is often not an easy situation. Besides,
the ALRS equipment requires a GPS antenna (delicate to install on
certain helicopters) and consumes electric power that is not always
available on the current planes. The geometric link between different

56 Michel Kasser
subsets (GPS antenna, inertial power station, ALRS) is a delicate
metrology operation, but fortunately it can be checked by the airborne
measures themselves if the software of calculation foresees it.
• The survey by ALRS is an active technology that doesn’t require, in
any aspect, lighting by the sun. There are no limitations therefore to
timetables of flight, other than those dictated by the security of the
aerial navigation. Flights are necessarily performed at low altitude,
therefore in zones with little problem of flight authorization (out of
the commercial air space), but which on the contrary are more and
more difficult to get over cities. But this possibility of working in the
morning, in the evening or in winter doesn’t present the same comparative
advantage now that one may use digital cameras, whose light
sensitivity is such that one can acquire excellent pictures without difficulty
with a low level of ambient light (low sun, flight under clouds).
As long as the question is to provide some DTM, such flights under
weak lighting are quite acceptable and competitive with the ALRS,
but the current problem is that one very often asks also for an aerial
image acquisition to serve as a basis for photo-interpretation, and even
the production of orthophotographies, and this requires good sun
lighting on the other hand. However, the ALRS generally cannot
provide a picture, in complement of the DTM: it is a tool to provide
DTM and nothing else. It doesn’t allow one to discern in a simple
way a house from a tree, for example, which limits its field of application
quite a lot. And if one adds a camera in the plane, considering
the height of flight it leads to a very significant image quantity, so that
one would not know how to deal with the present means in order to
make a mosaic or an orthophotography, even though all necessary
data are available.
• Interactions of the ALRS with vegetation are interesting and numerous.
To the list of problems, let us note that echoes obtained in the
high vegetation are very difficult to assign to a specific layer, that
is one works with the first or the last echo detected. On the other
hand, in forests the ALRS is the only technique that can provide,
in practically all types of forests (even tropical), a DTM of the
ground through leaves and branches. It presents a major interest
therefore for planning in equatorial zones, where the hydrology is
dominant and cannot be correctly processed without such data.
(See Figure 1.7.1.)
• An interesting feature of the ALRS resides in its capacity to measure
some echoes even on very small objects. The most spectacular example
is that of high-tension power line surveys. It would be impossible in
photogrammetry to survey lines, not because one doesn’t see them
(with a digital camera one sees easily even thin wires thanks to the
considerable dynamics of the picture), but because there is no means
to aim at the cable when the stereoscopic basis is parallel to the line,

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Airborne laser ranging systems for DSM 57
Figure 1.7.1 Two raw profiles obtained by the ALTOA® ALRS in French
Guyana (tropical vegetation around 40 m high). One notes that the
shots ranging to the ground describe very finely the topography, and
that in such circumstances a photogrammetric survey using the tops
of the canopy and subtracting a constant value would (1) ignore
important morphologic features such as trenches and (2) induce
large errors as the height of the canopy is far from constant.
which is necessarily the case for a linear survey of this type. In hightension
power line surveys by ALRS, it is possible to survey almost in
an entirely automated way lines and the zones of land and vegetation
that are close, which permits the identification on time of the interventions
of lopping that could be necessary.
• In most other domains, there are few differences between obtaining a
DTM by ALRS or by photogrammetry. Some authors consider that
in urban situations the ALRS presents significant advantages, but one
can note many counter-examples, and one may specify that the multiimage
matching (automatic correlation with more than two images)
on images of large dynamics in the city also provides excellent results,
with advantages and drawbacks that are different.
• We must note that error models are not at all the same, and that
neither of the two techniques really surpasses the other. For example
punctual mistakes are rare in photogrammetry, and numerous in ALRS
(electric lines, birds, reflection on planes of water, etc.). The precision
of measurement of a building may be also analysed in different ways
in the two cases: the automatic matching will easily find the edges but
will be in difficulty because of the hidden parts, the ALRS won’t
describe the edges correctly because of the width of the analysis spot.

58 Michel Kasser
For example, with regard to measures of pure altimetry, one cannot
establish a net benefit in terms of precision, the ALRS being locally
exact, but not being capable of identifying ditches or very important,
although small, streams on such sites. The data provided by ALRS or
by automatic image matching in photogrammetry are not originally
structured. Numerous studies are in progress to structure them in an
automatic way at least for the simple cases (e.g. buildings). And in
this domain photogrammetric methods use extensively the possibilities
of automatic analysis of every image, whereas the ALRS data are
much more difficult to analyse.
1.7.3 Perspectives, conclusions
One is therefore in the presence of a new technology, whose optimal use
in cases probably must be deepened again, but that one has nevertheless
to take into account from now on for data production (Ackermann, 1999).
The ALRS must be considered as a complement to photogrammetry, especially
suitable in some cases:
• surveys under vegetation;
• linear sites DTM and very fast supplying of narrow zones;
• high-voltage power line surveys;
• bare surface DTM.
There are a great many studies in progress to improve the fruitfulness of
this technique, and costs will probably soon become clearer, considering
their present instability.
References
Ackerman F. (1999) Airborne laser scanning – present status and future expectations.
ISPRS Journal of Photogrammetry and Remote Sensing 54, pp. 64–67.
Baltsavias P.E. (1999) A comparison between photogrammetry and laser scanning.
ISPRS Journal of Photogrammetry and Remote Sensing 54, pp. 83–94.
1.8 USE OF SCANNERS FOR THE DIGITIZATION OF
AERIAL PICTURES
Michel Kasser
1.8.1 Introduction
The present need for digital pictures destined for photogrammetric
processing is probably not going to stop growing in the next few years.

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Scanners for aerial image digitization 59
It was at first bound to developments in the digital orthophotography
market, from the 1980s. This development is far from finished, especially
because users are now able to handle without difficulty large digital
data quantities on low-cost personal computers, and particularly pictures.
So in a lot of urban GIS (geographic information systems) where data
must frequently be updated, it is current practice to work on a basic layer
formed by an orthophotography, that is not costly and therefore can be
often changed. The vector layers are then locally updated, from the
orthophotography, directly by the user himself. This evidently creates an
important market for digital aerial pictures. In addition, since the beginning
of the 1990s many software developments have been made, intended
to do all the photogrammetric restitution directly on PCs, transformed
thus in digital photogrammetric workstations (DPW, described in §2.5) of
lower and lower cost. Users of such DPW are no longer only societies
of photogrammetry, but are more and more technical users coming from
sectors quite external to photogrammetry, who themselves do the restitution
of objects that interest them. The diffusion of the DPW also creates
a demand for digital pictures, demand that is likely to increase for a few
years.
This need for digital pictures is currently satisfied in two ways: by digitization
of traditional silver halide pictures, and by the more and more
frequent use of digital aerial cameras (see §1.5). Pictures obtained by these
cameras have much better performances (radiometric and geometric as
well), but the cameras’ rarity has made it necessary for several years to
use scanners to digitise the new images acquired by traditional aerial
cameras (which are in general very reliable and of quite long life), and
these devices will remain necessary for a long time to allow the use of old
pictures.
We are going to analyse the techniques used by these scanners in order
to understand their shortcomings and their qualities. These materials themselves
are evidently also in regular evolution, but this evolution is notably
slow and the technologies used seem steady enough, probably because
there were no innovations in the domain of sensors applicable to these
devices for some years. We describe here the situation in the year 2000:
there are two classes of scanners, adapted to aerial pictures 24 × 24 cm.
There are those that have specifically been developed for photogrammetry
that are very precise, and thus very costly considering their low diffusion
(Kölbl, 1999), and to the contrary these are scanners of A3 format, less
precise but for a large public, much cheaper, and that can also be used.
The specification of these scanners is as follows: to allow the processing
of aerial pictures 24 × 24 cm, pictures on paper or on film, an analysis
pixel smaller than or equal to 30 m, in colour or in black and white,
with a good geometric precision. The possibility of processing some original
roll film directly is also an important specification for a part of the
market.

60 Michel Kasser
1.8.2 Technology of scanners
1.8.2.1 Sensors
Sensors used by off-the-shelf devices in 2000 are all based on chargecoupled
devices (CCDs, already seen in §1.5), being combined with an ina-plane
analysis of images. Photomultipliers were previously used with an
installation of images on a drum, which was not as easy, but this generation
of equipment is no longer available. These CCD are used in three ways:
in linear CCD, in matrixes, or possibly in TDI linear CCD. Let’s look at
these sensors in detail:
• The linear CCD are used in order to be able to scan at once with a set
of 10,000 or 12,000 detectors, either on only one linear CCD, or while
joining several shorter linear CCD. To get an analysis of colour, one
uses three of these parallel linear CCD juxtaposed, each equipped with
one of the three RGB filters. The group formed by these linear CCD and
the necessary optics is then displaced according to only one axis in relation
to the picture to be digitized, either it moves before the stationary
image, or the inverse. The scan of a whole picture requires several
successive passes, which therefore have to be perfectly connected.
• CCD matrixes used have the order of 2,000 × 2,000 pixels. There are
much larger matrixes, but given their high cost they are not a good choice
as their use would not appreciably accelerate the process. The detector
and its optic move in a sequential way according to two measurements
in front of the image to be processed, in order to cover all the useful surface
(it is necessary according to the size of the chosen digitization pixel
to cover up to 30,000 × 30,000 points of analysis), and there again the
mechanical displacement must permit an excellent connection between
the individual pictures that will make up the whole image.
• The linear CCD functioning according in TDI mode (TDI for ‘time
delay integration’, an inauspicious enough acronym because it explains
nothing). One exploits an oblong matrix (for example 2,048 × 96
pixels), and one uses it like a linear CCD (here of 2,048 pixels). While
making it advance regularly during the digitization as if it were a
normal linear CCD, one transfers charges produced from a line to the
following one (here 96 times), precisely at the same speed as the
displacement of the picture in the plane of the CCD. Thus a whole
set of charges recovered at the exit has been generated by only one
point of the analysed picture. So these charges have been produced by
many successive detectors (here 96), which homogenises the responses
of all detectors to a remarkable degree. It is similar to the way of
working that is described in §1.5 to perform the forward motion
compensation on matrix airborne cameras. One gets therefore a very
regular response from all detectors during the scan.

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Scanners for aerial image digitization 61
These devices present different advantages. For example, the time of integration
of a pixel facing the analysed photograph will be much longer for
a matrix than for a simple linear CCD, which will permit one to use a
less powerful lighting to illuminate the film, and will prevent undesirable
thermal effects due to the powerful lamps. The analysis of the colour by
three neighbouring linear CCD equipped with filters is simpler to achieve
than with a matrix, for which it is necessary to commute a set of filters
sequentially before every acquisition of an elementary zone. On the other
hand, if filters are put down directly on linear CCD, which is generally
the case, it is not possible to modify them, and there is no means to regulate
differently the lighting of each channel, which is possible with a matrix
system. Obviously it is necessary that the focusing of the optics be carefully
tuned, and with linear CCD systems it must be the same for the three
linear CCDs, which is not easy considering differences of wavelengths and
therefore of diffraction effects, which are very appreciable for extremely
small pixel sizes.
Let us note that irregularities of detector radiometric response may obviously
be corrected by a preliminary calibration, but that those that subsist
(dust particles, calibration errors) will create periodic and annoying artefacts:
• for linear CCD, some parallel strips will be displayed on the whole
document, among which one will also note those due to the successive
passes of linear CCDs;
• for matrixes it will be due to the repetition of errors according to a
regular paving, and of radiometric discontinuities between successive
positions of the matrix. These shortcomings will be generally far less
spectacular than for linear CCD.
Besides, behind every CCD there are special electronics (voltage-current
amplifier, digital to analogue converter) that must be optimized so that the
reading noise of the CCD is as low as possible, with a digital sampling
ranging from 8 to 12 bits. But this very high quality sampling is not so necessary
considering the noise of the photographic process itself, which does
not justify more than 6 useful bits. One will find normally all classic defects
of the CCD (echoes, blooming . . .) that are described in the corresponding
technical literature (Kodak, Dalsa, Phillips, Toshiba, Thomson . . .).
1.8.2.2 Mechanical conception
To displace an optic as a whole and to reposition it elsewhere within some
microns is not a simple operation. It is also one of the major technological
difficulties of scanners. That one uses linear CCD or matrixes doesn’t
create major differences in this respect. It is therefore mainly problems
of mechanics, that are generally solved using mechanisms having some
extremely reduced play, achieved in materials only giving a weak coefficient

62 Michel Kasser
of differential thermal dilation between the various sub-assemblies: one
does require from this mechanics only that it be extremely reproducible
in its errors. One proceeds to a very tidy calibration of the whole while
observing a regular and known pattern with a very high precision (patterns
on glass plate, known to about 1 m). One then deduces a set of correction
parameters to apply to the different elementary pictures assembly in
order to reach a precision compatible with the specifications (generally,
some m). But it is necessary to be very prudent with the ageing of these
structures, because of unexpected effects of dust on movements, or because
of any play that may develop and compromise the validity of tables of
correction parameters as well.
1.8.3 Size of analysis pixel
The available pixel sizes are very variable, starting at 4 m on the best
resolution devices up to more than 300 m when one achieves a coarse
sampling. Generally these large pixel sizes are reached by regroupings of
data obtained on the smallest possible analysis pixel. This generalized use
of a very small pixel and its regrouping by software is also used to rectify
the geometry of under-pictures between them, which without re-samplings
are still very expensive in time calculation and in memory space.
Recommended sizes of pixel evidently depend on the quality of the image
to be digitized and on the photogrammetric work to be performed. In
§1.9, where Christian Thom studies problems bound to the signal/noise
ratio of photographic emulsion, one will see that the smaller the pixel, the
more the signal/noise ratio deteriorates, and this well beyond the possible
defects of the scanner. A size of 30 m is satisfactory in most of the
studies of aerotriangulation type, DTM, orthophotography, etc. If one uses
smaller sizes (e.g. 15 m), gains in precision are often modest (Baltsavias,
1998) but at a high cost in terms of computer complications.
1.8.4 Radiometric quality, measure of colours
Considering the quite mediocre radiometric quality of photographs (with
a fidelity to the original object that is weak considering the chemical process
used), it is certain that there are not many conceptual difficulties in
achieving an analysis of images that practically does not bring any data
deterioration. In particular the restitution of colours, in such conditions,
looks more to the operator’s artistic sense (to provide a document satisfying
the customer’s eye) than to a rigorous respect of physical laws. The
available devices offer a large palette of tools in order to best balance the
RGB components. Let us note, however, that some mechanical defects can
drive to a small geometric colour component shift, which will be able to
generate some local artefacts especially visible on contrasted objects with
straight edges, linear or of a size close to the pixel size.

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1.8.5 Large A3 scanners
Scanners to the format A3 are available on the market, which are
therefore extensively capable of digitizing a whole aerial photograph,
and intended for the technical public in general. They are incomparably
cheaper than the specialized devices for photogrammetrists (around
50 times less) and it is interesting to note their possibilities of use.
Those available have to the date of writing, sizes of active pixel from
30 to 40 m, using a triple linear CCD with RGB filters, which permits
a digitization in only one pass and therefore a good geometric homogeneity,
some geometric errors ranging to 2 pixels that generally create
an affine distortion. It is to be noted that such distortions are also typical
of films, because of processes that they undergo at the time of the
development and drying, and that these errors are systematically modelled
by one additional unknown in phases of aerotriangulation. It is therefore
possible to use such scanners for certain photogrammetric studies
not requiring the maximal precision, and a fine assessment of their
limits and the temporal stabilities of error models is to be done for each
of them.
References
Radiometric and geometric precision 63
Kölbl O. (1999) Reproduction of colour and of picture sharpness with photogrammetric
scanners, findings of OEEPE tea scanner test, Proceedings of tea OEEPE
Workshop on Automation in Digital Photogrammetric Production, Marne-
La-Vallée 22–24 June, pp. 135–150.
Baltsavias E.P. (1998) Photogrammetric film scanners, GIM, vol. 12, no. 7, July,
pp. 55–61.
1.9 RELATIONS BETWEEN RADIOMETRIC AND
GEOMETRIC PRECISION IN DIGITAL IMAGERY
Christian Thom
1.9.1 Introduction
One of the first problems which the digital picture user is confronted with
is the size of the pixel that he is going to use for his scan. Intuitively, he
feels sure that, the smaller the step of the scan, the better will be the precision,
at least relatively, of the result, at the cost unfortunately of a greater
data volume. But generally he does not know that this better resolution
will also be paid for, as we shall see, in terms of radiometric quality. This
loss of radiometric precision also has an indirect but certain consequence
on the geometric precision. One will understand this, according to the
principle that ‘who can do more, can do less’ (one can always gather some

64 Christian Thom
small pixels to build bigger ones . . .). Nevertheless, one does not risk
getting a poorer result, paradoxically with small pixels than with big ones.
But as the size finally chosen is still the result of a compromise between
the geometric precision and the cost/volume of data/time processing,
it is clear that one must take into account the effect of the radiometry on
geometry to find the best compromise.
What is true for digitized pictures is true for digital pictures, that is to
say those provided by digital cameras, and this is because of two points.
First, a better geometric resolution itself has a cost, because it intervenes
directly, and fairly linearly, on the cost of the image acquisition: it is not
a question of a simple adjustment of the scanner, but is rather like the
choice of the scale in the classic case. Second, digital picture radiometric
quality is much better than that of the digitized pictures (under usual conditions
of digitization). One may easily understand that the aforementioned
effect is more crucial in this case.
A poor radiometry has obvious effects on other aspects than the
geometric precision, for example aesthetics and the interpretability of
the picture; they go far beyond the scope of this chapter because they are
too subjective to be modelled in a rigorous manner. Yet, they are not
completely different because the geometric precision that one can reach
in a picture certainly has an influence on its interpretability, and maybe
on its aesthetics.
1.9.2 Radiometric precision
This notion is relatively simple. Radiometry is the measure of the energies
given out by the objects of a scene. Its precision is therefore very definite,
as for any measure. However, in the context of this survey, the radiometry
in itself is still not accessible to us. Indeed, if the digital picture sensors are
almost always radiometric, this is not the case with the digitized film, where
the digital data of the picture are functions of the radiometry, monotonicgrowing
and limited, but not well known, and that, besides, depend on the
conditions of development of the emulsion. Fortunately, it will only have
little impact on our analysis, because we try to value the precision of
localization of visible detail in the images, and this precision will always be
a function of the ratio between the noise and the contrast of the detail. This
ratio may be valued more or less directly in the image.
If the notion is simple, its evaluation is not, especially in the case of
the digitized pictures. If models of noise are well known for the digital
sensors, they are not in the case of digitization, where the noise of
the scanner, noises bound to the emulsion and its process superimpose
themselves. Here, we will use data that we acquired from experiments (1),
and from measures on the digital camera of IGN-F (2). However, it is
necessary to investigate the origin of these noises, because some aspects
have an impact on our topics.

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Radiometric and geometric precision 65
1.9.2.1 Digital camera
The noise model here is quite simple. The sources of noises are:
1 the reading noise of the sensor, due to the electronics of sampling,
essentially Gaussian;
2 the photon noise, due to the corpuscular nature of light, according to
a law of Poisson;
3 differences of pixel sensitivity (may be corrected by calibration);
4 differences of dark current (may be corrected also by calibration).
In general, it is the photon noise that dominates. It grows according to
the square root of the signal, and its value depends on the total number
of photons that every pixel can contain. For example, in the case of the
KODAK sensor used at IGN-F, this number is 85,000, and the signal/noise
ratio at full capacity is 300.
1.9.2.2 Digitized pictures
Sources of noises are here more numerous and not very well known:
1 noise coming from the sampling unit, which depends on the equipment
used, the size of pixel, the level of grey obtained, etc.;
2 noise coming from the emulsion.
Let us look at this second point in more detail. One knows that the photographic
process is based on detection of light by ions of silver, then to an
amplification of the signal by the developer, that makes every nucleus
created by a photon detected in a grain of silver of a certain size grow
(some microns). The film is then analysed by the scanner that values its
optic density, that is to say the proportion of light that passes between
grains of silver. One immediately sees numerous consequences:
• The response of the film is not linear. Indeed, the photochemical process
of grain production is not linear, because several photons are necessary
so that a grain can be created, producing low sensitivity of the
film to low illuminations. But even though one may suppose this
process as linear, when the density of silver grains grows, they make
‘shades’, when a grain overlaps another. The marginal sensitivity for
a proportion of R grain will thus be 1 R. This gives us a function
according to the illumination i of R(i) 1 exp (ki). The optic
density, which is proportional to the logarithm of 1 R, is therefore
also more or less proportional to the illumination of the emulsion.
• If one considers the middle of the dynamic range of the film (R
1/2), for a size S of the pixel analysis and a characteristic size of grain
of s, if i expresses the number of photons detected, one has:

66 Christian Thom
Surface of the pixel: S 2
Surface of the grain: s 2
For small values of i one notes that k s 2 /S 2
For R 1 ⁄2, i log (1/R)/k log (2) S 2 /s 2
The signal to noise ratio is
r √i √(log 2) * S/s.
(1.33)
Let us take, for example, the following values: S 20 m, s 1 m:
one finds r 16.6. Recall that under similar conditions, a sensor
directly digital may benefit from a signal/noise ratio of about 150.
This gives an indication of the problem . . .
If we consider the values obtained, it seems justifiable to neglect in
what follows the scanner’s own noise in as much as we don’t know
it, and as it depends on the type of device used.
One also notices in this formula that r is proportional to the dimension
of the analysis spot. In general the spot of analysis on a scanner
is bigger than the step of sampling to avoid any aliasing, which slightly
improves the previous values, at the cost of a poorer MTF (modulation
transfer function) of course.
Finally, this formula gives us an idea of the ratio between the
quantum efficiency of the film and of the CCD sensors. Indeed, our
experience shows us that conditions of image acquisition (exposure
time, relative aperture) in the two systems are practically the same.
One sees that on a pixel of 20 m, the film detects 280 photons,
whereas on a pixel of 9 m, the CCD detects about 20,000 of them,
which corresponds to a ratio of 350 in sensitivity . . .
These very simple equations explain why the CCD sensors can be smaller
than the usual focal planes of classical cameras, and that their pixels are
themselves smaller, but that they retain nevertheless an enormous advantage
in terms of radiometric quality. The entire problem is to exploit it to
the fullest, to compensate their relative apparent lack of resolution.
1.9.3 The geometric accuracy
We will concern ourselves here in the geometric accuracy in the picture,
and not in the accuracy of objects in the scene. This means that we will
make abstraction of all problems of systematism bound to the image acquisition,
even if they may be important (e.g. the aerial cameras based on
linear CCD sensors), where the poor knowledge of parameters of external
orientation of the sensor leads for every line of the picture to a poor precision
of pixel localization.
One can distinguish two different ideas in this domain. First of all, the
precision of positioning of a detail in the picture, this detail being able to

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be punctual, linear, or area, this one going back to the linear case in
general because we position its limits most of the time. In the same way
the punctual is often the intersection of two linear details (corners of
building, for example), although there are also some merely punctual
details. The fact that the detail is distributed in general on several pixels
obviously helps its localization, because one can have several evaluations
of the measured position, and therefore take the mean value.
Then, there is the more delicate problem of the separation of two nearby
details, or resolution, which affects the interpretability of the picture more
than the precision itself, but which we mention here because it is more
demanding in terms of pixel size. Indeed, it is clear that even with pictures
of very good quality it is impossible to separate details less than two pixels
apart, whereas in terms of localization precision, one can without difficulty,
in the same conditions, aim at a few tenths of a pixel. If the size of
the pixel is evidently an element determinant of this precision, it is not
the only one. The resolution of the optics is another. All situations can
present themselves between two extremes:
• fuzzy pictures over-sampled with pixels which are too small;
• high-resolution pictures under-sampled with pixels which are too large.
Both cases can be found for example with a scanner either poorly set up
or not tuned, and the second with digital cameras not having adequate
optics. These situations evidently include the ideal case of pictures sampled
while respecting the limit of Shannon, but it is very rare, because the characteristics
of optics are not constant in their whole field of view, and
therefore a regular sampling does not permit the criteria of Shannon to
be respected everywhere.
One is confronted therefore, in general, often with no ideal and sometimes
with unknown situations. We will examine some simple typical cases,
in general at the extreme ranges of the possible, the intermediate situations
being always more complicated.
1.9.3.1 Precision of localization
Radiometric and geometric precision 67
The case of under-sampled pictures
With regard to the punctual details, the precision is easy to determine:
there is no means to determine the position of the detail inside its pixel
(see Figure 1.9.1). We deduce a RMS precision in x and y of 0.29 pixel,
independent of radiometric precision. In the case of a linear detail, the
precision that one can get depends on the a priori knowledge one has on
the nature of the detail (is it straight?), and of its orientation in relation
to the axes of the picture. The worst case is evidently a detail parallel to
one of the axes of the picture, and having the same precision of 0.29 RMS

68 Christian Thom
pixel. On the other hand, for a differently oriented detail, the distribution
of the energy in the different pixels crossed by the detail permits the precision
to be improved, which depends then on the characteristic dimension
of the detail by which one can consider it as straight. Since one uses the
value of pixels crossed, radiometric precision will have an importance, but
this is difficult to evaluate. With regard to area details, the problem is to
position the edge of the surface. This situation, fortunately more frequent
than the previous (fields, roads, buildings, etc.), is more favourable, because
sub-pixel position of the edge is function of the quantity of energy received
by the pixel containing the edge. If we simplify the problem taking an
edge parallel to the y axis, of c contrast, one understands that its subpixel
position in x can be calculated by: dx dg/c, dg being the difference
of radiometry in relation to the pixel of reference. The precision on x is
therefore directly bound to the radiometric noise. To give an idea, with a
contrast of 1/10 normalized to the value of saturation of the sensor, one
gets in the case of the film digitized at 20 m a noise with a rms of 0.6
pixel, which means that no profit is possible, and in the case of the digital
sensor 1/15 0.07 pixel, which is substantial. Let us push a little farther
the problem of the film. Indeed, why use smaller pixels to the digitization?
Radiometry
In input
Values of
pixels
Figure 1.9.1 Limit of zone, under-sampled situation.
C
dx
x

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Radiometric and geometric precision 69
The noise grows as 1/S, and therefore if one is only interested in a pixel,
the precision will be the same, whatever the value of S. Fortunately, it is
necessary to take into account the fact that for a unit of length of
the detail, one can take the mean value of the position of the detail as
many times that it contains pixels. One will have therefore a precision
proportional to s.(S/L) 1/2 /c, where L is the usable dimension of the
detail. In fact one cannot decrease the size of the pixel indefinitely without
reaching the limit of resolution of the optics, and therefore moving to
the next case.
The case of over-sampled situations
We study here the case where any transition of radiometry is progressive.
All detail is represented therefore on several pixels. There, all the previous
cases are reduced to the case of one edge. Indeed, a linear detail is described
by two successive edges, their characteristic dimension being, however, the
half of one edge (the transition of an edge is in fact the integral of that
of a linear detail, i.e. the point spreading function (PSF), projected on the
axis perpendicular to the detail). We will then look at the localization of
a zone of constant gradient of width D and useful length L. The D size
is bound to the width of the PSF of the optics. One can consider that it
is the half-maximum width of this one in the case of the side of an area
detail, and of one half of this one for a linear detail. Our model here is
very simple, but it will be nevertheless sufficient to analyse the problem
in a qualitative manner (see Figures 1.9.2 and 1.9.3).
Radiometry
L
C
Figure 1.9.2 Limit of zone, over-sampled case.
S
D

70 Christian Thom
Radiometry
L
The precise position (sub-pixel) in x is given by the mean value of the
zone where the gradient is constant, divided by this gradient:
g
Dx
LD
The noise on this value is characterized by:
x g
S
√LD
C
Figure 1.9.3 Linear detail, over-sampled case.
S
D g
S2
C L S2
C
D
C g S
C D
L .
. (1.34)
(1.35)
Here again, in the case of a digitized image, the size of pixel S also intervenes
into the denominator, and therefore is independent of this one, but
is a function of the grain size.
It is necessary to note that one should not overuse the L parameter.
Indeed, it is rare that one can suppose that a detail is linear on an important
length. Besides, we assume we know its orientation, which is not in
general the case, and introduces a supplementary unknown, and therefore
more imprecision.
Let us recall that in the case of the linear detail, the assessment of the
position can also be done with the other side of the detail, and that D is
one half of the previous case. Thus the benefit is in relation to the edge
length, a factor 2 at the end.
D

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General case
In fact, in practice one is most often confronted with intermediate situations,
where the PSF of the optics is the order of the pixel, or of a pixel
fraction, and is not known with precision, or varies one point to another,
etc. The methods of precise positioning described may give in this case
mediocre results with residual bias. This is due to the fact that the PSF is
itself poorly sampled. Yet these methods always bring an improvement in
relation to the situation seen in the case of under-sampled pictures whose
results can be considered therefore to contain major errors.
Conclusion
One can extricate several findings from what we have just seen:
• to work with well-sampled pictures is important if one wants to fully
benefit from this kind of technique;
• however, to position the edge of area details, a poor sampling is sufficient;
• the use of this kind of technique on the digitized images is useless,
except for very contrasted details, the noise in this type of pictures
being far too dominant.
1.9.3.2 Spatial resolution
Radiometric and geometric precision 71
Thin detail detection
Contrary to what one commonly believes, it is not impossible to see in a
picture details smaller than the size of the pixel. Just note that it is sufficient
that the contrast of the detail, multiplied by the ratio of the surface
occupied by the detail to that of the pixel, is in correct relation with the
radiometric noise.
An example of this property is given in Figures 1.9.4 and 1.9.5. These
are pictures taken on the same zone, a pond over which passes several
high-tension power lines. The first image is an excerpt of a picture coming
from one digital camera of IGN-F. The second image is a digitized image.
Sizes of ground pixel are similar, around 75 cm. On these two excerpts,
one distinguishes cables of the thickest line (probably doubled), but the
finest line is visible only on the picture from the digital camera. The section
of cables is 3 cm, that is to say of the order of the 1/20th of the pixel
size! One sees that here also, a good signal to noise ratio in pictures allows
one to compensate a poor geometric resolution.

Figure 1.9.4 IGN-F digital camera.
Figure 1.9.5 Digitized image.

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Radiometric and geometric precision 73
Resolving power
It seems at first that radiometric quality is not able in any way to compensate
for a poor geometric resolution. Indeed, two details situated in the
same pixel will never be able to be separated. This proposition is obvious,
but it is necessary to state it however.
One can view the problem in the opposite direction, that is to say to
interrogate oneself on the real resolving power of pictures whose radiometric
quality is insufficient. Traditionally one is supposed to discern
two details (choose for example bright ones) if they are separated in the
picture by dark pixels. It is clear that in the case of details poorly
contrasted, and in pictures of poor quality, the bright pixels because of
the presence of details will have a certain chance of being darkened
by the noise, and the dark pixel that separates them will have a possibility,
to the contrary, to be brighter. The inverse situation may happen,
where an object will be split falsely. One sees that one rejoins here the
problem of segmentation, since one poses the question: ‘Does this pixel
belong to this object?’
Let’s study a concrete case, for example: the segmentation of a supposed
homogeneous zone. We deliberately choose a simple algorithm, where a
step on radiometry determines the assignment to one zone or to another.
If the contrast between the two zones is c, the step will be placed to c/2
(one supposes the noise to be independent of radiometry). What is, in these
conditions, the probability that a pixel is poorly classified? It is a simple
problem of statistics, bound to the interval of confidence. The success of
the segmentation process and its precision will obviously depend on this
parameter, as a non-trivial function of the algorithm used, and a priori
knowledge that one has from structures in the picture (straight edges for
example).
One can see in Figures 1.9.6 and 1.9.7 the same zone in two simultaneous
image acquisitions, one with a digital camera of IGN-F, the other
with a traditional camera. If one pays attention to the ridges of roofs, one
notices that they are clearly delimited in the digital picture, whereas some
edges are indiscernible on the digitized picture. This loss of visibility will
evidently have consequences on the precision of its restitution, notably
with automatic means. It is unfortunately impossible to quantify this here,
because it evidently depends on the algorithms used.
In Figures 1.9.8 and 1.9.9 one can see the result of the filter of extraction
of contour from Adobe Photoshop for example. It clearly appears
that the extraction of roof edges can be performed more easily and
more precisely on the digital picture. Note the side of roads in the shady
regions.
To illustrate even better the influence of radiometric quality, and
its interactions with geometry, see Figures 1.9.10 and 1.9.11: the same
picture is presented here, but after it has been under-sampled by a

Figure 1.9.6 IGN-F digital camera.
Figure 1.9.7 Scanned image.

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Figure 1.9.8 IGN-F digital camera, contours.
Figure 1.9.9 Scanned image, contours.

76 Christian Thom
Figure 1.9.10
Under-sampled scanned picture.
factor 2. This operation, as it averages pixels, decreases the noise, and
one sees that the process of contour extraction now works better, but its
result will be evidently less precise, being obtained with a pixel twice as
large.
We didn’t mention here the question of the sampling technology, but it
has an influence of course. When the PSF is larger than the pixel, the
contrast between two nearby details tends to soften, and therefore the
restitution of the two details will be sensitive to the noise. When it is
smaller, one doesn’t note an appreciable effect.
Conclusion
It is clear that for what concerns the geometric resolution, radiometric
quality brings much with regard to the detection of details. It has an influence
on the separation in the case of weakly contrasted details, that is to
say whose contrast is the same level as the noise present in the picture. It
is necessary to mention that these details are frequent in urban zones,
materials of construction often being of similar albedo (different types of
coating, for example), and the frequent shade zones.
1.9.4 General conclusion
Figure 1.9.11
Contours from Figure 1.9.10.
The impact of radiometric quality on the geometric quality is still not easy
to evaluate. The problem is complicated by the fact that it depends on
algorithms used for the restitution, and on the adequacy of the picture
sampling. Yet, it is real in most cases. The comparative studies conducted
on the digital camera of the IGN-F and on digitized pictures, to scales
ranging from 1/15,000th to 1/30,000th, clearly show that the very large
available dynamics of the CCD camera allows one to reach the same uses
as the digitized silver halide picture, this in spite of a pixel of a size about

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Radiometric and geometric precision 77
twice as large. But this coefficient of 2 is only valid in this range of scales,
and other studies should specify its value for smaller pixels: this coefficient
doesn’t depend indeed only on radiometric quality, but also on the
type of object being surveyed.

2 Techniques for plotting
digital images
INTRODUCTION
This section deals with the ways of extracting the 3D data from the images.
Some considerations, here also, are not really specific to the use of digital
images, but they must nevertheless be examined within the scope of digital
photogrammetry, as in the case of aerotriangulation, which now offers
some new aspects with digital images (such as the automatic extraction of
link points, for example). We will start with a summary of the image
processing techniques seen from the point of view of the photogrammetrists,
i.e. when the geometry is critical (§2.1). In the same way, the techniques
of data compression are analysed for the specific case of digital images
whose geometry, here too, is critical (§2.2). A summary about the use of
GPS in airplanes (§2.3.1) is then presented: this is not specific to digital
photogrammetry, but it deals with many practical problems of today’s
photogrammetry. Then a short presentation about the aerotriangulation
process is proposed (§2.3.2). Then, under the title ‘automatization of the
aerotriangulation’ is presented the automatic extraction of link points, and
their use to compute the index maps (§2.4), which is the first step when
processing a set of images. Then we close this chapter with a survey of
the techniques used for digital photogrammetric workstations (§2.5). The
automatic cue extraction methods, available at the time of completing this
book, for planimetric items (the vegetation, the buildings, the roads, . . .)
are still very uncertain and cannot be yet considered as operational, thus
we have not presented them, as they are still in the research laboratories.
Of course in Chapter 3, the automatic extraction of the altitude will be
explained, with all the induced problems of DTM, DEM, DSM: this is the
only operational process available that uses all the possibilities offered by
digital images (and it is the simplest one, any other cue extraction requires
much more human interpretation from the operator, and thus is also much
more difficult to implement on a computer).

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2.1 IMAGE IMPROVEMENTS
Alain Dupéret
2.1.1 Manipulation of histogram
The improvement of the image contrast is a process that tends to make
the images more beautiful to use, on sometimes subjective criteria. Even
if we cannot necessarily say how a good image should look, it is often
possible to say if it is optimized, sufficiently, for example, to see some
details. There are therefore several techniques of image improvement, but
manipulations of a histogram probably represents one of the most used
methods.
2.1.1.1 Definition of the histogram of a image
In statistics, the histogram is a bidimensional representation of the h function,
called density of frequency, defined by:
h(x) h i
if x ∈[a i1, a i]
Image improvements 79
∞
∞
h(x) 0 if x < a0 or if x > ak verifying h(x) dx 1.
(2.1)
In image processing, the histogram is therefore the diagram representing
the statistical distribution (h i, n i ) where h i represents the ith level of possible
colour level among the N possible values and n i the number of pixels
presenting value h i in the digital image. By misuse of language, the h function
is often called a histogram. This function is always normalized in
order to be used like a law expressing the probability that a colour level
n i has to be present in the whole image. The grey level is considered therefore
like a random variable that takes its values in a set of size N, being
often 256 by reason of the usual coding of the elementary information of
every channel on a byte. The new digital sensors, whose intrinsic dynamics
ranges over several thousand levels require more space for storage.
A priori, no hypothesis can be proposed on the shape of a histogram
and it is quite normal to have a multimodal histogram, presenting several
attempts. A corresponding histogram to a Gaussian distribution is possible
but more current in the case of satellite images. The only certainty concerns
the extent, of which it is recommended that it is as large as possible, up
to possibly using the 256 available levels. (See Figure 2.1.1.)
2.1.1.2 Visual representation of data
In practice, when data present a weak dynamic at the level of making their
exploitation difficult, transformations intended to improve the contrast are

80 Alain Dupéret
Figure 2.1.1 Excerpt of an aerial image and the histogram associated with this
image.
still possible and will be presented. These will act by modifying coded
values of the image, either while adapting the transcodage table (Look-
Up-Table) used by the screen for the colour display. The user should keep
in the mind also, that when an image is displayed on a computer screen,
its contrast also depends on the adjustment of the monitor but also and
especially on the spectral sensitivity of the eye, that presents a maximum
for green-yellow colour levels; for a given wavelength variation of d, it
implies a weaker colour level perception for the red or the blue-green, situated
on the edges of the curve of spectral sensitivity of the eye, which is
variable from one observer to another. Other factors are to be taken into
account also, such as the prolonged observation of an intense colour
provoking a transient colour aberration due to the retinal pigments, the
global environment of the point observed that can make appear a more
or less clear colour, as well as side effects.

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Image improvements 81
2.1.1.3 Generalities on the modification of histogram
Manipulations of histograms are punctual operations that transform an
input image I(x, y) into an output image I′(x, y) according to a law I′(x,
y) f [I(x, y)]. The f function is presented as a graph for which abscissas
are colour levels of I, and the ordinates colour levels of I′. They are often
destined to fit the dynamics of input images that are initially not contrasted
enough, too clear or too dark. This redistribution of colour levels of the
image can lead to some interpretation errors when the f function is nonmonotonous
or discontinuous:
• the horizontal sections in the graph of f lead to information losses;
• some vertical jumps provoke discontinuities resulting in false contours
or aberrant isolated points;
• some negative slopes lead to local inversions of contrast.
The histogram of the image I′ is centered in ac b and its width multiplied
by a. In image processing software, the parameter ‘brightness’ can
be associated to the b value and the parameter ‘contrast’ to the value a,
slope of the curve transforming Di into Di′. (See Figure 2.1.2.)
2.1.1.4 Dispersion of the dynamics
As the raw image, considered here with pixels coded on one byte, never
takes all possible values between 0 and 255, it results in a contrast default
even though one knows that the eye can only discern a few tens of grey
levels on a screen. Thus it is convenient to spread out the initial dynamics
[m, M] in the largest possible interval [0, 255] with the help of the operation
DI ′ (DI m) × [255/(M m)]. This operation does not provide
n I
b
D I′
c
D I′ = aD I + b
D I
D I
n I′
Figure 2.1.2 Manipulations of histogram.
D I′
Histogram of the output image I′

82 Alain Dupéret
any new information and is more a strategy of display on the screen than
an interpolation technique. It is often proposed at a more elaborate level,
giving better results, by calculating two levels (min and max), as
min
0
h(x)dx h(x)dx , 0.01 or 0.00,
(h represents the function of distribution of colour level levels in the image).
Then the dispersed display ranges from [min, max] to [0, 255].
An interesting variant exists when the input histogram is unimodal and
relatively symmetrical and determines min and max according to the statistical
properties of the colour-level distribution, as illustrated in Figure 2.1.3.
For a multispectral image, the dispersion is achieved independently on
the different channels, at the risk of provoking a modification of the colour
balance, each channel having initially a dynamics that is its own for a
given raw image.
It is quite possible to proceed to a non-linear redispersion of the dynamics
whose advantage is to reinforce contrasts for a part of colour levels of a
histogram: logarithmic shape to reinforce the dark zones, exponential one
for the clear zones. Often used, this strategy has the drawback of decreasing
contrasts in the zones of the histogram not affected by the strong curvature
of the transfer curve but it does allow a more faithful replication of
the way the eye responds to different levels of brightness. (See Figure 2.1.4.)
A strong slope on the central curve means an accentuation of contrasts in
the corresponding zones, which are here the numerous dark parts of the
right image. The thinning of contrasts in the clear parts is not here visually
bothersome.
2.1.1.5 Equalization of a histogram
The equalization of a histogram is a method that looks for an equiprobable
statistical distribution of levels hi , which means to put ps (s) c where
c is a constant.
The relation pr (r) dr ps (s)ds being valid for all values, the search for
T in R T(S) leads therefore to
s
0
r
c ds pr (r) dr ⇒ c 1
0
255
max
s
s 0
p r (x) dx ,
which provides the sought-after relation. (See Figure 2.1.5.)
The previous formulation presumes that r and s can take continuous
values. With the digital images, it may be only a finite number of values in
the interval [r, rdr]. When redistributing this interval on a larger domain,
the principle of conservation of the number of pixels means therefore that

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Figure 2.1.3 For a given raw image on the left, the visual results are given for an interval [min, max] being worth
successively [moy, moy], [moy2, moy2], [moy3, moy3] toward the right.

84 Alain Dupéret
Figure 2.1.4 Non-linear redispersion of the dynamics: on the left, the original
image, on the right, the modified one through the curve in the
centre.
Figure 2.1.5 Application of the method of equalization of the histogram.
only the concerned pixels are redistributed and that the histogram cannot
be virtually flat.
For an image I constituted of n colour level levels quantified on N levels
D I(k), these last are transformed by the law
D I′(k) (N 1) p I D I(k) where p I n I
n ,
n I representing the number of pixels of values D I(k). As the results D I ′(k)
may be decimal, the method implemented in the software rounds off then
to the nearest integer value, which leads to having several D I(k) levels
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D I(k) from which it originates, thus justifying the non-uniformity of the
histogram. To palliate this effect, some methods redistribute from pixels
the more represented in colour levels toward the insufficiently represented
neighbouring values, until reaching a balanced population for every quantification
level.
If the number of colour levels in I′ is therefore lower than in I, all
possible levels not being necessarily represented, this technique allows the
best possible dynamics and gives strong contrasts. Nevertheless, it may not
give visually good results, colour levels of objects photographed not necessarily
being suitable for such a hypothesis.
2.1.1.6 Obtaining a histogram of any shape
The operator can very well choose to have the function ps (s) as the final
histogram, which means then
s
0
r
ps(y) dy pr(x) dx ,
0
which permits one to define s according to r.
Generally speaking, the following steps are achieved:
Image improvements 85
• equalization of the original image y 1 g(r) p r(u)du;
• equalization of the desired histogram y 2 f(s) p s(u) dv;
• application of f 1 (function that is calculated easily by tabulation) to
the histogram g(r), or f (s) g(r) ⇒ s f 1 g(r) (the two histograms
being identical).
2.1.1.7 Improvement of local contrast
The previous methods are global manipulations of the image and do not
take into account the possible disparities of contrast or quality that may
exist within any given image. To avoid this inconvenience, techniques of
local improvement of contrast have been developed. In the neighbourhood
of each pixel of size n × m that is going to be displaced progressively on
all pixels of the image, the local histogram is calculated in order to be
able to apply methods previously mentioned, such as the equalization or
the assignment of a shape of a given histogram (e.g. Gaussian shape). As,
each time, only a new column or a new line appears with the transfer of
a pixel in the image, it is possible not to repeat the complete calculation
of the histogram while using calculations of the previous iteration.
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86 Alain Dupéret
Thus, for a given image, the definitive assignment of a colour level for
a pixel requires each time a process of manipulation of the present value
histogram in a neighbourhood of given size.
The statistical process operates on sub-images of variable size and is
going to use the mean intensity and the variance that are two applicable
properties to model the image appearance. For a mean radiometric value
moy(i, j) inside a mean window centred on the pixel of coordinates (i, j),
and a radiometric variance of (i, j) inside the same neighbourhood, the
value of the radiometry in I may be modified in I′
I′(i, j) A × [I(i, j) moy(i, j)] moy(i, j) with
A kM
(i, j)
, scalar value called gain factor (2.2)
M: mean value of the radiometries in the whole image k ∈ ]0, 1[
Figure 2.1.6 Improvement of the local contrast.
(a) In terrestrial photogrammetry, conditions of lighting are sometimes far from optimum.
Effects of over- or under-exposure are decreased by a local improvement of contrast, but
beyond a given threshold, the noise of image becomes unacceptable.
(b) The image on the left presents clear zones in the top-left corner (hot spot) that can be
suppressed while imposing the image in exit on the right to present a Gaussian histogram
inside a window whose size is chosen by an operator.

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so as to heighten the contrast locally for the weakly contrasted zones, A
being inversely proportional to (i, j).
The size of the processing window is a predominant criterion:
• if small (3 × 3 to 9 × 9), it permits the strongest possible improvement
of the local contrasts, the side effect being to increase the image noise
(see the pair of images on the Egyptian temple of Dendera shown in
Figure 2.1.6);
• if large (50 × 50, 100 × 100 . . .), it allows the averaging of the values
of colour levels on large zones, thus decreasing the disparities of brightness
in the different places of the image, but its local effects are then
less visible (see the pair of images on the zone of Agen).
These methods are often used to improve the similarity of two images
acquired at different dates; in aerial imagery, it allows the reduction of
Figure 2.1.7 Improvement of contrast.
Stereogram of the raw images in the upper part, and of images with local improvement of
contrast on small size windows; even though the increased noise appears unacceptable on
an image, the stereoscopic examination in zones of shade is nevertheless possible and limits
the need to order a new aerial acquisition or the exploitation of other images.

88 Alain Dupéret
disparities of radiometry between two distinct images when they must be
merged into a mosaic, or even an ortho-image.
Beyond the simple process of a unique image, the use of a couple of
stereoscopic images can be very helpful at medium or large scales, especially
when zones of shades embarrass the perception of objects (see Figure
2.1.7).
The application to multi-spectral images (several channels) is more delicate,
as previously seen, processes having to be applied independently to
each channel to provide a coherent result. In the case of colour images,
the representation can be performed in a colorimetric reference with red,
green and blue main components; every coordinate of a pixel along one
of these axes is the colour level it has in the corresponding spectral band.
The set of points corresponding to pixels in this reference forms a cloud
in which one searches the main axes along which data are best distributed.
This is performed using the method of classification in main
components often used in remote sensing.
The operation of local improvement of contrast can be achieved while
passing in the frequency domain and using techniques of homomorphic
filtering.
2.1.2 Filtering – suppression of the noise
2.1.2.1 The noise in the images
The signal in the image is composed of information, superimposed with
noise; in the case of an image, it may be the noise inherent to the digital
sensor used at the time of the acquisition, of the nature of the photographic
document if it is a document that was digitized. Methods already
presented processed every pixel independently of the neighbouring pixel
value, and also have the effect of increasing without distinction noise and
information in the images, which justifies the processes devoted to
decreasing the noise. This noise is formed of pixels or small isolated pixel
groups presenting strong variations with their environment.
In practice, images have a certain spatial redundancy, the neighbouring
pixels often having some colour levels of very close values. If some general
hypotheses on the noise are made (additive, independence of the signal
and greatly uncorrelated), it is possible to achieve operations of filtering
intended to limit the presence of the noise in images while achieving lowpass
filtering, linear or not, in the spatial or frequency domains. The
justification of the low-pass character of the filter is as follows.
Usually, the noise in images is not correlated with the signal level, and
presents therefore a fairly uniform spectral distribution. As for images the
part of low frequencies is more important than that of high frequencies,
a moment happens where the signal is dominated by the noise, from where
comes the idea of threshold beyond a limiting frequency. The elimination

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Spectral density
Image spectrum
F c
Noise spectrum
Frequency
of this part of the spectra of course destroys a certain part of the signal
which results in a image with little texture and fuzzier contours.
This process can by calculation of Fourier transform of the image on
which is applied a process entrenching all the frequencies beyond the
threshold value, then by an inverse Fourier transform. (See Figure 2.1.8.)
There are two general types of noise (see Figure 2.1.9):
• additive noise:
– of pulse type, whose detail is to tamper randomly with some pixel
colour levels to produce a ‘pepper and salt’ effect in images;
– of Gaussian type, if a variation of colour level following a centred
Gaussian probability density is added on colour levels of the image
– this is the most current type;
• multiplicative noise, as for example that resulting from a variation of
illumination in the images.
2.1.2.2 Use of filtering by convolution
Methods of filtering are numerous and are often classified by type: linear
filtering, non-linear, morphological (opening, closing), by equation of diffusion
(isotropic or not), adaptive by coefficients, or adaptive windows.
The use of convolution operators in the spatial domain (the image) transforms
a I(x, y) image into I′(x, y) using a square window of odd dimension
2n1, moved on the image, by a matrix A with coefficients ai, j so that
I′(x, y) ai, j I(xi, yj) where n i, j n .
i, j
Image improvements 89
Figure 2.1.8 Beyond F c , the spectrum of the image is dominated by the noise.
(2.3)
2.1.2.3 Linear filtering in the spatial domain
The simplest filtering consists in finding the average of pixels situated in
a window of given size and to apply it to the central pixel, and to repeat
this operation in every point of the image.

Figure 2.1.9 Types of noise in images.

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The application of a filtering is a question of convolution of an image
by a kernel, assimilated to the mask of the transfer function of the filter,
whose coefficients can be adapted by the user according to the objective.
Examples of kernels for low-pass filters:
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1
1
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1
or filter by the average,
Image improvements 91
or Gaussian filter.
(2.4)
This type of filtering is adapted to the elimination of Gaussian noise more
than that of pulse noise. The way to use the filter by the average can be
optimized while keeping in mind the processes applied to points of the
neighbourhood; for Gaussian filter, it may be decomposed into two unidimensional
filters. These artifices permit the number of operations performed
in order to achieve filtering to be reduced. (See Figure 2.1.10.)
The use of such a filter decreases high spatial frequencies, as strong as
the size of the window is large. One thus should be careful not to tamper
with objects that one wishes to preserve in the image, because their contour
becomes less and less meaningful with the progression of this filtering.
Moreover, these processes generate side effects the larger the size of the
window or the number of applied iterations is more important. This filtering
therefore considerably degrades the contours and makes the image fuzzy,
with some exceptions, as for example when the signal is stationary and
the noise Gaussian.
2.1.2.4 Non-linear filtering in the spatial domain
Linear filtering has the main drawback of processing in the same way the
parts of signal carrying information and noise, which sometimes justifies
the use of non-linear processes, more able to attenuate the aberrant values
of pixels whose colour level is too distant from the neighbouring ones.
Also called filtering of rank, these methods replace the central or current
pixel by one of the values selected from pixels of the Vxy neighbourhood
of it (x, y): pixel of minimal, maximal or median value . . .
This type of method is more robust with regard to the noise of the
image and has the advantage of assigning an existing value without calculating
a new one.

Figure 2.1.10 Gaussian filtering.
On the left, an image digitized at 21 m on an aerial photograph. The homogeneous zones, including noise, contain a random texture
that does not constitute a useful signal. In the centre, the original image after Gaussian filter. If the noise was attenuated, contours also
became fuzzy. On the right, an image of a digital camera from IGN-F: zones are naturally weakly noisy because of the nature of the
sensor and its very good dynamics.

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2.1.2.5 Median filter
In this process, the value assigned to the pixel is the statistical median
value in the filtering window, whose number of elements must therefore
be odd. The median is indeed the best evaluation of the mean value of a
whole sample, less sensitive to aberrant values, and it is supposed here
that they correspond to the extreme values of the histogram inside the
mask of the filter. (See Figure 2.1.11.)
This process allows one to eliminate the isolated values that correspond
to tips of pulse noise and preserve contours of objects more efficiently than
the linear filters. Nevertheless, distortions misled by this filter on objects
increase with the size of the window used. This filtering is therefore especially
advisable when images present a noise of pulse type, and therefore
important variations of weak extent. Some implementations use a mask
in the shape of a cross centred on the current pixel, a shape which is
preferred to the square shape to limit distortions in the image.
2.1.2.6 Adaptive filtering
Filters are said to be adaptive in the following cases:
Image improvements 93
Figure 2.1.11 Median filter.
Use of the median filter on the previously used raw images. It presents as a main defect to
round corners and to smooth lines whose width is less than a half of that of the filter.
• coefficients consider every term of the filter by the average, by a term
that decreases with the similarity between the considered pixel and the
central pixel of the window;
• the window is chosen either in shape or in size.

94 Alain Dupéret
The filter of Nagao, relatively unknown, provides nevertheless very good
results in the case of aerial images, in particular in urban sites. It is structured
in four steps:
1 a window 5 × 5 around the central pixel is divided into nine windows
of nine pixels each;
2 the first two models are each declined in four diagrams deduced from
the one presented by successive rotations of 90°, 180° and 270°;
3 the homogeneity of every window is measured, with the help of an
indicator of the radiometric variance type;
4 the central pixel is replaced by the most homogeneous average within
the nine zones.
The filter obtained strongly smoothes textures without tampering too much
with the contours of objects in the images. (See Figures 2.1.12 and 2.1.13.)
The filter of Nagao has the defect of smoothing the thinnest features of
the image. Some algorithmic variants therefore exist to find the most applicable
indicators of the homogeneity measure. The size of windows used,
the weighting type used and the shape of masks of application can be
adapted empirically in such a way as to get the best filter for the preservation
of the lines, the corners or the suppression of the noise.
Figure 2.1.12 Filter of Nagao, first step.
Figure 2.1.13 Filter of Nagao applied (right) to the left image.

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2.1.2.7 Filtering in the frequency domain
The filter in the frequency domain takes place in three steps:
• calculation of F(u, v) TF(I(x, y)); in general, it is fast Fourier transform
that is used on the base image;
• multiplication by H(u, v), transfer function of a ad-hoc filter: G(u, v)
H(u, v)·F(u, v);
• obtaining the image filtered by inverse Fourier transform of G(u, v).
The time of computation becomes a major parameter that must be considered,
before any use in an operational context. Practically sometimes one
uses, instead of direct and inverse Fourier transform, a square mask whose
coefficients are the discrete elements of the transfer function of the frequency
domain filter. Butterworth filters, low-pass exponential and Gaussian are
the more frequently evoked, even though, for the meantime, only few
applications in digital photogrammetry use them.
Homomorphic filtering is also usable to correct irregularities of lighting
of an object. Note that a I(x, y) image can be written as the product of
e(x, y)·R(x, y), where e is the function of lighting that rather generates
some of the low frequencies at the time of the calculation of Fourier transform,
and R is the reflectance that rather generates some high frequencies
by the nature of objects that composes it.
The two effects are made additives by creating a logarithmic image so
that:
ln (I(x, y)) ln (e(x, y)) ln (r(x, y)). (2.5)
Homomorphic filtering will increase the high frequencies and reduce the
low frequencies to the point of reducing variations of the lighting while
details will be reinforced, thus permitting a better observation in the dark
zones of the image (see Figure 2.1.14). The function of transfer is the
shape
H( x , y )
with values as s 1, 0 128 and A 10, these parameters being joined
as follows to the H and L parameters and by
L
1
1 exp (s0) A, H 1 A .
1
1 exp (s 2 2
√x y 0)
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96 Alain Dupéret
Γ H
Γ L
H(r)
2.1.3 Improvement of contours
Points of contours form the majority basis of the information included in
the images, probably more than textures, which play nevertheless an essential
role, in particular for the perception of the relief. The recognition of
an object is performed most often only from its contours. The difficulty
resides in the subjective notion that the user presumes to define the utility
and the importance of a contour. The multiplicity of contour detectors
results from the variety of the studied images and from the type of application.
2.1.3.1 Methods of the gradient
This first category is based on the use of the first derivative of the luminous
intensity. The most often met operators are constructed below from
models:
1
0 1
0
1
0 0
1
1
1
1
r = (ω x 2 + ωy 2 ) 1/2
Figure 2.1.14 Homomorphic filtering.
0
0
0
1
1
1
5
3
3
5
0
3
5
3
3
Gradient Roberts Prewitt Sobel Kirsh (2.6)
The three last operators have the advantage of being less sensitive to the
noise than the traditional derivative, but unfortunately also create more
drifts. As each are directional, it is usual to construct similar filters to
detect the contours in the eight possible directions.
1
2
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0
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.

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The convolution by Sobel operators
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2
1 ,
2
1
0
1
0
1
(that would be to the number of eight by displacing the whole coefficients
by a quarter of a turn for every new filter) allows one to detect zones of
contours in a given direction.
The superposition of the four images obtained with the above-proposed
filters achieves an image of the amplitude of the gradient; for every
pixel I (x, y) , the maximum found in the intermediate images of coordinates
(x, y) is selected. The presence of a contour can be decided in
relation to a threshold on this value. (See Figure 2.1.15.)
It will often be interesting to reduce the noise of an image with methods
like the median filter or the filter of Nagao, which will not prevent the
contours from suffering from an approximate quality if they are too noisy,
thick and non-continuous.
Figure 2.1.15 Sobel filter.
1
0
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98 Alain Dupéret
2.1.3.2 Methods of passage by zero of the second derivative
This second category is based on the survey of the passage by zero of
second derivatives of the luminous intensity in order to detect contours.
If zeroes of the second derivative constitute a closed network of lines, the
second derivatives are generally very noisy. To palliate this inconvenience,
it is possible to widen the support of the mask used, to select only passages
by zero accompanied by a strong slope of the signal, or again to filter
contours obtained after the detection.
There are several types of Laplacian:
0
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1
0
1
0
.
(2.7)
After the application of these masks to the image, one detects contour
points by the detection of passages by zero of the image obtained. The
singleness of the passage by zero provides contours whose thickness is
directly one pixel. (See Figure 2.1.16.)
One shows that, if the noise is Gaussian, the most suitable operator is
constituted by the Laplacian of a Gaussian defined by:
G(x, y) 1
1
1
1
1
8
1
2 4 2 x2 y 2
1
1
1
1
2
1
2 exp x2 y 2
. (2.8)
Another method calculates passages by zero of the directional second
derivative in approximating the intensity in a window by a polynomial
whose coefficients are calculated by convoluting images with masks. One
can calculate second derivatives in the direction of the gradient and find
2
2
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1
2
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Figure 2.1.16 Use of a Laplacian filter (right) on the left image.

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points of contour as passages by zero of these directional second derivatives.
For a point of coordinates (i, j), the coefficients approximating the
intensity in the basis
1, i, j, (i 2 2
3), ij, (j 2 2
3), (i 2 2
3)j, i(j 2 2
3), (i 2 2
3), (j 2 2
3)
are the following:
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0
0
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1
1
0
1 ,
1
2
1 .
1
6 1
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0
1 ,
1
1
1 ,
1
6 1
1
1
1
4 1
2
1
1
4 1
0
1
2
0
2
1
0
1 ,
(2.9)
Sometimes the computation cost of these latter processes is considered
too high, so that approaches of compromise between speed and performances
have been developed; thus for example the Deriche filter, which
possesses an infinite pulse response of the shape f (x) c × exp ( |x|)
permitting therefore an implementation by means of separable recursive
filters. 2D filtering is obtained by the action of two filters crossed in x and
y, and the filtering of the noise with the help of a function of extension
(generally a Gaussian of the same standard deviation as the one considered
for the detector). (See Figure 2.1.17.)
0
0
0
0
0
0
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1
1 ,
1
2
1 ,
1
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1
1
2
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Figure 2.1.17 From left to right: image of contours by a Laplacian, original
image, and contours by the gradient of Deriche.
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100 Alain Dupéret
2.1.4 Conclusion
The image improvement can often be performed by techniques of convolution
with the suitable filters, of finite extension, and thus that permit an
implementation on the image as linear operators. The improvement of
an image aims at improving its aesthetic through subjective criteria.
The improvement of the image may also use:
• techniques of manipulation of colour-level levels using properties of
the histogram to which the user can give the shape that he wants;
• techniques of filtering in order to reduce the noise and to improve the
contours in the image. The most frequently used methods are nonlinear.
Bibliography
Haralick R.M. (1984) Digital step edges from zero crossing of second directional
derivates. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.
PAMI 6, no. 1, January, pp. 58–68.
Deriche R. (1987) Using Canny’s criteria to derive a recursively implemented
optimal edge detector. The International Journal of Computer Vision, vol. 1,
no. 2, May, pp. 167–187.
2.2 COMPRESSION OF DIGITAL IMAGES
Gilles Moury (CNES)
2.2.1 Interest of digital image compression
The digitization of pictures offers a large number of advantages:
• possible processing by powerful software;
• reliability of the storage (on CD-ROM, hard drives . . .);
• errorless transmission (thanks to the error-correcting codes).
Nevertheless, it has the inconvenience of generating often large volumes
of data. To give examples, a spatial remote sensing picture acquired by
the Spot satellite in panchromatic mode represents a volume of: 6,000 lines
times 6,000 columns at 8 bits/pixels 288 Mbits. A classical digitized
aerial image, scanned with a 14 m pixel size, provides 2,048 Mbits.
Of course the first goal of the engineer, when designing the data flow
system, should be to define the number of effective bits by pixel through
a careful consideration of the noise in the image, so that the expected
noise level is at the level of the last bit, for example. But quite often the

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Compression of digital images 101
final figure is larger, in order to be able to cope with situations significantly
different from the nominal one, which means very often one or two
bits beyond what should be optimal.
Considering limitations that apply in most systems on capacities of
storage and/or transmission, it is necessary first to reduce to the minimum
the quantity of necessary bits per pixel to represent the picture. To
compress, one chooses the representation that provides the minimum
number of bits, while preserving in the picture the necessary information
for the user. The efficiency of the compression will be measured by the
rate of compression, that is the ratio between the number of bits of the
picture source to the number of bits of the picture compressed.
The compression of pictures is possible for the following reasons:
• Data pictures issued from the instrument of image acquisition present
a natural redundancy that doesn’t contribute to information and that
it is possible to eliminate before storage and transmission. One can
compress pictures efficiently therefore without any loss of information
(so-called reversible compression). Nevertheless, we will see in the
following that this type of compression is limited to relatively low
rates of compression (typically between 1.5 and 2.5 according to the
content of the image).
• Besides, the end user of pictures is interested, in general, in only part
of the information carried by the picture. It is what one will call the
relevant information. It will therefore be possible to compress pictures
more efficiently again while removing non-relevant information (socalled
compression with losses) and this to the same satisfaction of
the user. Rates of compression will be able to reach much higher figures
(up to 50 in certain applications of very low quality). Of course, the
level of distortion due to the compression will be a function of the
rate and the performance of the algorithm used.
For every application, there will be a compromise to find, according to
limitations of resources (storage, transmission), between the satisfaction of
users (the quality of pictures being inversely proportional to the rate of
compression used) and the quantity of pictures that can be stored and/or
transmitted.
2.2.2 Criteria of choice of a compression algorithm
Criteria to take into account for the choice of an algorithm of compression
and a rate of compression are very varied and depend in part on the
targeted application. Among the most generic, one can mention:
• The type of images: pictures of photographic type including a large
number of levels of gray or colour (8 to 24 bits by pixel), or artificial

102 Gilles Moury
pictures including only a few levels of gray (e.g. binary pictures of
type fax). These two types of pictures require very different algorithms.
For normalized algorithms, one can cite: the JPEG standard for the
photographic pictures, the JBIG standard for the artificial pictures with
few gray levels and the standard T4 and/or T6 for the black and white
fax. We will now consider only the pictures of photographic type.
• The level of quality required by the user: this ranges from a strictly
reversible compression need (case of certain applications in medical
imagery) to needs at a very low quality level (case of certain transmission
applications of pictures on the Internet). The tolerable loss
level and nature will have to be refined for example with the user
through validation experiments for which several levels and types of
degradation will be simulated on the representative pictures of the
application. The type of degradation (artefacts) is going to be rather
the function of the algorithm, and the level of deterioration the function
of the compression rate.
• The type of algorithm: normalized or proprietary. Principal advantages
of normalized algorithms are of course compatibility and permanency,
with the ascending compatibility guarantee as well. The major inconvenience
is the slow evolution of norms that means that a finalized norm
is very rarely the the most effective solution available.
• The type of transmission or type of access to the decompressed picture:
sequential or progressive. In the first case, the picture is transmitted
in block to maximal resolution; in the other case, one first transmits
a low-resolution version (therefore very compact) that permits the user,
for example, to choose in a data base and then select a full resolution
version. Algorithms using transformation (DCT, wavelets . . .) permit,
among others, progressive transmissions.
2.2.3 Some theoretical elements
2.2.3.1 Correlation of picture data
In a natural picture (as opposed to an artificial grid), the correlation
between neighbouring pixels is very high and decreases according to the
Euclidian distance between pixels. The correlation decreases very quickly
with the distance and often becomes negligible to 5–10 pixels of distance.
To compress a picture efficiently, and therefore to avoid the need to code
and to transmit several times the same information, the first operation to
achieve is always to locally decorrelate the picture. We will see several
types of decorrelator in the following. The simplest decorrelation to achieve
consists, instead of coding every pixel p(i, j) independently of its neighbours,
in coding the difference: p(i, j) p(i, j1) with i an indication of
line and j an indication of column.

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2.2.3.2 Notion of entropy
The entropy is a measure of the quantity of information contained in a
set of data. It is defined in the following way:
• consider a coded picture on k bits/pixel, in which every pixel can take
2 k values between 0 and 2 k 1;
• the entropy of order 0 of the picture (denoted H 0(S)) is given by the
formula:
H0(S)
2k1 Pi log2 i0
1
Pi , (2.10)
where Pi is the probability that a pixel of the picture takes the i value.
The theory of information (see reference [1]) shows that H0(S) gives, for a
source without memory and therefore decorrelated, the mean minimal number
of bits per pixel with which it is possible to code the picture without
losing information. In other words, the maximal compression rate that it
will be possible to reach in reversible compression is given by: CRmax
k/H0 (S).
To illustrate the notion of entropy, let’s take four different picture types:
1 a uniform picture where all pixels have all the same value, H 0(S) 0,
this picture contains no information;
2 a binary black and white picture of the type of those processed by fax
machines:
H(S) P white log 2
1
P white
Compression of digital images 103
P black log 2
. (2.11)
One has H(S) < 1. In practice, P black

104 Gilles Moury
• entropy of the picture source: H 0(S) 6.97;
• entropy of the picture after decorrelation of type [p(i, j) p(i, j1)]:
H 0 (S) 5.74.
The more efficient the decorrelation, the weaker will be the entropy of the
picture after decorrelation and the higher will be the rate of compression
attainable by reversible coding of data decorrelated. Nevertheless, rates of
compression attainable remain relatively low (of the order of 1.5 to 2.5
on pictures of remote sensing of the type from the Spot satellite).
2.2.3.4 Compression with losses
When one searches for some compression rates higher than CRmax, which
is the most current case, one is obliged to introduce losses of information
in the chain of compression. These losses of information are achieved in
general by a quantification of decorrelated data. For a given picture and
algorithm of compression, there is a relation between the achieved rate of
compression and the errors introduced in the picture by the compression/
decompression. This curve, called ‘distortion/rate’ has the typical shape
given in Figure 2.2.1.
The distortion is often measured quantitatively by the standard deviation
of the compression error, given by the formula:
Degradation
(standard deviation of the error)
2.0
1.5
1.0
0.5
0
1
CR max
2 3 4 5 6
Compression rate
Figure 2.2.1 Typical ‘distortion rate’ curve.

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1
NM N
i1
M
p(i, j) p′(i, j)
j1
2
(2.12)
for an image with N lines, M columns and a null mean error of compression,
which is the most general case (p′(i, j) being the value of the pixel
rebuilt after compression/decompression).
The maximal level of tolerable distortion by the user of pictures fixes
the maximal usable rate of compression on the mission. To compare performances
of two algorithms of compression, one should draw the
‘distortion/rate’ curves of the two algorithms and this on the same image(s),
as the performance (rate) of an algorithm vary considerably from one
picture to another according to the entropy of data to compress.
2.2.4 Presentation of various types of algorithms
Compression of digital images 105
A complete presentation of the various types of compression algorithms
can be found in references [1], [2] and [3]. We will give the general principles
below and describe some algorithms among the more used.
2.2.4.1 General architecture
Any compression system can be analysed in three distinct modules (see
Figure 2.2.2): the decorrelation of the source picture, the quantization of
decorrelated values and the binary code assignment.
1 The decorrelator allows the redundancy of data to be reduced. In practice,
there are a large number of methods, more local, to decorrelate
the incoming pixels. We give some examples farther on (DPCM, DCT
and wavelet transform). This phase of picture processing is perfectly
reversible. At the end of this first phase, the process of compression
hasn’t in fact begun, but data were decorrelated so that the following
processes (quantization, coding) are optimal.
2 The quantizer is the essential organ of the compression system. Indeed,
here the quantity of information transmitted is in fact going to decrease,
while eliminating all the information not relevant (in regard to the
utilization that is made of pictures) included in the data coming from
the decorrelator. Let’s recall that non-relevant information is a quantity
that only depends on the envisioned application(s). For example,
IMAGE
SOURCE
DECORRELATOR
DECORRELATED
DATA
QUANTIZATION
QUANTIFIED
DATA
Figure 2.2.2 General diagram of a compression system.
AFFECTATION
OF
CODES
BINARY
TRAIN

106 Gilles Moury
in the case of the Spot satellite missions, radiometric precision is not
relevant in strong transition zones (very contrasted contours). The
quantity of non-pertinent information eliminated by the quantizer must
be able to vary according to the application. We see therefore that the
quantizer plays the role of organ of command of the compression
system while allowing it to be used at different rates. The quantization
is the only non-reversible operation of the compression chain.
3 The assignment of codes (or more simply coding) has the role of
producing a binary stream, representative of the quantized values,
which will be transmitted effectively or stored for later transmission.
The rate of compression really reached by the system can be valued
in a realistic way only at the end of this module. Its role is to assign
to every quantized value or event a binary code that will be able to
be decoded without ambiguity by the decoder. This assignment can
be made more or less economic in terms of number of bits transmitted.
The most efficient codes are codes of variable length whose principle
is simple: to assign the shortest codes to the likeliest values (or events).
An example of variable-length code is the Huffman code, used in the
standard JPEG and MPEG. The implementation of the various methods
of compression will not show the three already mentioned modules.
Some modules will be able to be regrouped in only one (as is the case
for quantization and coding in algorithms using the vectorial coding).
The quantization module can also disappear as in the case of a
reversible compression method.
2.2.4.2 Reversible algorithms
There are two main classes of algorithms to achieve the reversible compression
of pictures: the universal algorithms capable of compressing any type
of data, and algorithms specifically optimized for pictures, these last giving
performances 20 to 30 per cent better in term of compression rate.
Universal algorithms
The most widely used is the Lempel–Ziv algorithm (LZ, LZ77, LZW) used
in the utilitarian zips, gzip, and pkzip and in formats of picture tif, gif,
and png. Its principle consists in marking sequences of symbols (characters
of a text, values of pixel) that repeat in the file. These sequences are
then stored in a dictionary that is brought dynamically up to date. Every
sequence (of variable length) is coded by a code of fixed length dependent
of the size of the dictionary (e.g. 12 bits for a dictionary of 4,096 elements).
This type of algorithm derives benefit from the correlation of the source
and adjusts itself in real time to the local statistics (by updating the dictionary).
Nevertheless, the coding of pixels being linear along the scan line,
one doesn’t benefit from the vertical correlation in the picture, and then

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Compression of digital images 107
the performance is not as good as that of specific algorithms that use correlation
in the two dimensions.
Specific algorithms
The most effective algorithm is the new JPEG-LS norm [4]. The block
diagram of this algorithm is given in Figure 2.2.3. It uses a 2-dimensional
decorrelator of predictive type (the most often used in lossless algorithms).
The value of the current pixel x is predicted from a linear combination of
pixels a, b, c (see Figure 2.2.3) previously encoded. The error of prediction
is then coded with the help of an adaptive Huffman code according
to the context (a, b, c, d) of the current pixel (analysed by the module of
context modelling). A coding by area is used in completely uniform zones.
On the Spot satellite image of Genoa (Figure 2.2.6) one gets the comparison
between universal algorithms and specific ones shown in Table 2.2.4.
Thus we may achieve a gain of about 30 per cent on the rate.
Source
Image
Context
modelling
Predictive
decorrelator
Coding by area
c
a x
Huffman
coding
Figure 2.2.3 Block diagram of the JPEG-LS algorithm and context for the
modelling and the prediction.
Compressed
image
Table 2.2.4 Various compression rates for 2 algorithms on the Spot image of
Genoa
Algorithm Rate of compression
JPEG-LS 1.65
Lempel-Ziv (gzip-9) 1.27

108 Gilles Moury
2.2.4.3 Algorithms with losses
These algorithms are classified, from the simplest to the most complex,
according to the three main types of decorrelators used: differential (DPCM),
cosine transform (DCT), wavelet transform (multiresolution).
DPCM
The differential decorrelator DPCM consists in predicting the value of the
pixel to code from a linear combination of values of its already coded
neighbours (see Figure 2.2 3.). The prediction error is then quantized with
the help of a non-uniform law adapted to the Laplace statistics of this
prediction residual. This type of algorithm, used on Spot satellites 1/2/3/4
to a rate of 1.33, has the feature of being very simple and to concentrate
errors of compression in strong radiometric transition zones (well
contrasted contours), zones in which the absolute value of the radiometry
is of low importance in remote sensing. Its disadvantage is its poor performance
in terms of ‘distortion/rate’ for rates ranging from middle to high
(>5) (see Figure 2.2.10), owing to a too local decorrelation of the signal.
For the compression with losses, the DPCM decorrelator has therefore
been abandoned to the profit of the DCT.
DCT
The DCT (discrete cosine transform) is the decorrelator most commonly
used in compression of pictures. It is the basis of many standards of
compression, among which the best known are:
• ISO/JPEG for still pictures ([5]);
• CCITT H261 for video conferencing;
• ISO/MPEG for video compression.
The DCT is one of the unitary transforms (see [1] for greater precision
on the definition and the interest of unitary transforms in compression)
used in compression to achieve the decorrelation. This transformation operates
on blocks of n × n pixels (n 8 in general) and achieves on these
blocks a Fourier transform of period 2n of which only the real part is
kept. The general diagram of compression based on a unitary transform
DCT is given in Figure 2.2.5.
The direct DCT transformation of a block 8 × 8 is given by the following
formula, where p(i, j) are pixels of the source picture and the F(u, v) are
DCTS coefficients representative of the spectral content of the block at the
different spatial frequencies:

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Image
source
Rebuilt
image
Cut the
image into
blocks 8×8
Concatenate
8×8 blocks
p′(i, j)
p(i, j)
F(u, v) 1
2 C uC v 7
i0
Direct DCT
Transform
Inverse
DCT
transform
F(u, v)
F′(u, v)
7
p(i, j) cos
j0
Compression of digital images 109
Quantization
Inverse
Quantization
Figure 2.2.5 Chain of compression by DCT transform.
(2i 1)u
cos
16
F*(u, v)
Variable flow
F*(u, v)
(2j 1)v
,
16
where C u (resp. C v) = 1/√2 if u = v = 0 and C u = C v = 1 if not.
In the transformed domain (spatial frequency domain):
Affectation of codes
(codes with variable
length)
Decodage
(2.13)
• the F(u, v) coefficients obtained are correctly decorrelated contrary to
source pixels of the block;
• coefficients that have a non-negligible amplitude are statistically concentrated
in a restricted region of the transformed plan, which greatly
facilitates the ulterior coding after quantization of these coefficients.
The quantization is a simple division by a quantification step of q. The
larger the q, the higher will be the rate of compression and vice versa. The
rate and therefore the error on the rebuilt data is controlled therefore by
the choice of the step. At the output of the quantization, a large number of
coefficients (F*(u, v)) are nul. A Huffman coding is used therefore on events
of type run-length adapted to this statistics. This coding, which is particularly
efficient, has been optimized during the studies on the standard
ISO/JPEG. This standard, of which a detailed description is given [6], is
used very extensively (80 per cent of images transmitted over the Internet
are compressed with JPEG).
The main drawback of algorithms with a DCT basis is due to the fact
that every 8 × 8 block is coded independently from its neighbours, which
creates problems of block adjusting after decompression. This phenomenon
(called block effect), invisible to the eye for weak compression rates
(< 8), can be bothersome for some picture-processing applications. It is
illustrated in Figures 2.2.6, 2.2.7, 2.2.8 and 2.2.9 that represent respectively:
the source picture, the compressed DCT/JPEG to a rate of 8 picture,

110 Gilles Moury
Figure 2.2.6 Excerpt of picture from Spot satellite (panchromatic mode) on the
city of Genoa – non-compressed original.
Figure 2.2.7 Picture of Genoa compressed with an algorithm of JPEG type to a
rate of 8 (rms 6.8).
a zoom on the source picture and the same zoom on the compressed picture
making clear the blocks effect. To suppress this block effect and to improve
again the decorrelation with regard to the DCT, one has recourse to algorithms
based on the decomposition in sub-bands (by wavelet transform)
described hereafter.
Wavelet transform
The approach of coding techniques in sub-bands is identical to that of
coding by unitary transform by block (DCT or other): analysing the signal

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Figure 2.2.8 Zoom on the non-compressed picture of Genoa.
Compression of digital images 111
Figure 2.2.9 Zoom on the picture of Genoa JPEG compressed to a rate of 8 (very
visible 8 × 8 block effect).
in different frequency components in order to code each of them separately.
Means used to get this decomposition are, however, different: in the
method by block a matrix 8 × 8 of transformation provides the different
frequency components, whereas a real filtering of the whole picture must
be achieved in the sub-bands technique. This decomposition in N subbands
takes place by means of a hierarchical filtering of the picture. The
filters used are determined from the theory of wavelets [7]. One thus
achieves a wavelet transform of the picture.

112 Gilles Moury
Advantages of decomposition algorithms in sub-bands by wavelets are
as follows:
• the decomposition of the picture in different spatial frequencies is made
globally on the picture (by a mobile window of filtering) and not by
8 × 8 block as in the DCT. Thus there are no problems of continuity
in borders of blocks on a decompressed picture;
• ‘distortion/rate’ performances are much better for the rates superior
to 8 (typically): improvement of 30 per cent to 50 per cent of the
compression rate for the same distortion level (see Figure 2.2.10);
• the progressive transmission of different resolution levels and the noise
removal is very easily integrable in this type of compression scheme.
For these different reasons, the JPEG committee has been reactivated to
define the JPEG2000 standard based on wavelet transform. This future
ISO standard should be completed in 2000 [8] and integrates a large
number of functions (random access to the compressed file, progressive
transmission, resilience to transmission errors, ascending compatibility with
JPEG . . .).
For these algorithms based on wavelet transform, the most effective
quantization/coding techniques are bit planes quantization and zero-trees
coding. The state-of-the-art representative algorithms are EZWS [9] and
SPIHT [10].
Comparison
One compares ‘distortion/rate’ performances of the three types of decorrelators
(DPCM, DCT, wavelets) through three representative algorithms,
on the Spot satellite picture of Genoa (Figure 2.2.6) (see Figure 2.2.10):
• DPCM: JPEG-LS algorithm in quasi-lossless mode [4];
• DCT: JPEG algorithm ‘baseline’ mode [5];
• wavelet: SPIHT algorithm [10].
2.2.5 Multispectral compression
The algorithms presented until now only take benefit from the intra-picture
correlation (or spatial correlation). In the case of a multispectral (or colour)
picture, it is also possible to exploit the correlation between the different
spectral bands. In the case of the Spot satellite pictures for example, which
include four bands (b1, b2, b3, mir), b1, b2 bands are very strongly correlated
on certain types of landscapes whose spectral content has only
moderate variations.
It is therefore interesting to achieve a spectral decorrelation then a spatial
decorrelation of the picture (the inverse order is also possible). A complete

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rms of the error
20
16
12
8
4
0
0 4 8
compression rate
12
analysis of all usable techniques can be found in [11]. The spectral decorrelator
can be of predictive type or by orthogonal transform. The optimal
transform to achieve this operation is the Karhunen–Loève transform (KLT).
This transform enables one to switch from a spectral coordinates system
[bi] where components are greatly correlated, to a reference [di] where
components are decorrelated and the information (energy) of the picture is
concentrated on a few components. An example of such a transformation
is that used in digital television (standard CCIR 601 [12]): transfer from
the system [R,V,B] to the system [Y,Cb,Cr], 80 per cent of information
is concentrated on the signal of Y luminance; signals of chrominance
differences (Cb,Cr) carry little information and thus can from then on be
under-sampled and/or compressed to higher rates than the luminance.
2.2.6 Perspectives
Compression of digital images 113
DPCM
DCT
Wavelets
Figure 2.2.10 Comparative curves ‘distortion/rate’ for DPCM, DCT, wavelets.
Beyond the compression by wavelet transform now extensively used and
which will be soon normalized (JPEG2000), different solutions are currently

114 Gilles Moury
underway to attempt to improve the ‘distortion/rate’ performances of algorithms.
Among these, one can cite:
• the compression by fractals [13] that, coupled to the decomposition
in sub-bands by wavelet, permits progress in the high rate range (> 30);
• the selective compression that consists in detecting in the picture, zones
of interest for the user, in order to apply to those a rate of compression
preserving the quality of the picture, while the remainder of the
picture can be compressed with a higher rate (e.g. on the Spot satellite
pictures, zones of interest are zones without clouds). The selective
compression opens the way to the more elevated rate used in many
applications. All the difficulty lies in the reliability of the detection
module.
References
[1] M. Rabbani, P.W. Jones, Digital Picture Compression Techniques, SPIE Press,
vol. TT 7, 1991.
[2] J.P. Guillois, Techniques de compression des images, ed. Hermès, coll.
Informatique, 1995.
[3] K.R. Rao, J.J. Hwang, Techniques and Standards for Image, Video and Audio
Coding, Prentice Hall, 1996.
[4] International Standard ISO-14495–1 (JPEG-LS).
[5] International Standard ISO-10918 (JPEG).
[6] W.B. Pennebaker, J.L. Mitchell, Still Image Data Compression Standard, Van
Nostrand Reinhold.
[7] M. Vetterli, J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995.
[8] http://www/jpeg.org (official site JPEG).
[9] J.M. Shapiro, Embedded image coding using zerotrees of wavelet coefficients
(EZW), IEEE Transactions on Signal Processing (Special Issue on Wavelets
and Signal Processing), vol. 41, December 1993.
[10] A. Said, W.A. Pearlman, A new fast and efficient image codec based on Set
Partitioning in Hierarchical Trees (SPIHT), IEEE Transactions on Circuits and
Systems for Video Technology, vol. 6, June 1996.
[11] J.A. Saghri, A.G. Tescher, J.T. Reagan, Practical transform coding of multispectral
imagery, IEEE Signal Processing Magazine, vol. 12, January 1995.
[12] ITU-T Recommendation 601, Encoding parameters of digital television for
studios, 1982.
[13] M.F. Barnsley, L.P. Hurd, Fractal Image Compression, Peters, 1993.

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2.3 USE OF GPS IN PHOTOGRAMMETRY
Thierry Duquesnoy, Yves Egels, Michel Kasser
2.3.1 Use of GPS in photographic planes
Thierry Duquesnoy
Use of GPS in photogrammetry 115
2.3.1.1 Introduction
In aerial images acquisition, the GPS (global positioning system), or any
other GNSS equivalent system (GLONASS, or the future GALILEO) may
be used in three distinct phases:
• the real-time navigation;
• the determination of the trajectory of the plane, more precisely the
determination of the position of the coordinates of the camera at the
time of the image acquisition;
• the determination of the attitude of the plane.
If these three aspects use the GPS effectively, they do not require the same
type of measure. The most original use concerns the measure of attitude
that we will describe farther.
We will recall briefly here that two types of GPS observations exist:
• the pseudo-distances that are measures of time of propagation of the
pseudo-random modulation of the signal;
• the measure of phase, performed on the wave carriers, and that is
performed on an identical but stable signal generated by the receptor
and locked on the satellite signal.
And two types of positioning exist, the absolute positioning and the relative
positioning. The precision of the positioning varies according to the
type of observations, from a positioning accurate at the level of a few
metres to a relative precision of the order of 2 mm ± 10 6 D to 10 8 D
using the measure of phase.
In the end of section (2.3.1.5), one will find a summary of the terminology
employed for the different uses of the GPS.
2.3.1.2 The navigation
The navigation is a priori the simplest mode. It uses the pseudo-distances.
At the time of the image acquisition, it is necessary to have the position,
in almost real time, of perspective centres in order to verify that the followup
of the axis by the plane is good and that the overlap rate is correct.
In absolute positioning, with a precision that is about ten metres (with the
SA switched off, as it is since May 2000), conditions are achieved. The
metric precision realized is by far superior to the 40 m with which pilots

116 Thierry Duquesnoy et al.
can hold the axis of flight. If a better precision is required, the differential
mode is necessary: several solutions may exist to get the differential corrections
in real time. One can use networks of stations that broadcast
corrections on different frequencies. One can arrange his own GPS receptor
on a known fixed station that sends corrections. And then there are differential
correction services via a geostationary satellite. This last process
seems best suited for airborne applications.
Let’s note that in differential navigation, the speed of the plane is known
to 0.1 knot, which is sufficient for photogrammetric applications.
For the overlap, it may be necessary to know the attitude of the plane
at the same time. We will describe these needs in the chapter dedicated to
the determination of attitude.
2.3.1.3 The determination of perspective centres for the
aerotriangulation
We saw that measures of pseudo-distances permit a metric positioning
when differential data are available. However, the necessary precision on
the determination of perspective centres must be at the same level as that
necessary for the photogrammetric process, typically 10 m × the scale of
the picture. A decimetre precision is therefore necessary to most photogrammetric
applications (scale varying from 1:5,000 to 1:40,000). This precision
cannot be reached with the exclusive utilization of pseudo-distances. But
the measure of phase is ambiguous as, while using the phase, one only
measures the fractional part of the cycle, the whole number of cycles separating
the receptor of the satellite being unknown.
Therefore there are two ways to improve the precision of the determination
of perspective centres a priori: improve the process of the pseudodistances
while using the phase, or be able to solve ambiguities in the
process of the phase.
The trajectography
This is a calculation in differential mode between a reference station of perfectly
known coordinates and the antenna and receptor on board the plane.
The process is based on the fact that phase data are less noisy than pseudodistance
data. Indeed, one considers that the noise of the measure is estimated
to be better than 0.1 per cent of the wavelength of the signal on which the
measure is made. Therefore, the noise on the pseudo-distances is metric while
the noise on the phase is millimetric. Thus one tries to improve the process
of pseudo-distances by decreasing the noise of measure, by a smoothing
process with the help of the phase measurement. This is the trajectographic
mode. In this mode no initialization is necessary. One gets by this method
an internal consistency within one axis inferior to the decimetre. But then,
the precision between neighbouring strips is no better than some metres.

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The resolution of ambiguities on the flight
Again, this is a positioning in differential mode. In the case of two fixed
receptors, the resolution of ambiguity is possible without too many difficulties
for baselines of several hundred kilometres. But it is much more
difficult when one of the GPS receptors is mobile.
An algorithm developed by Remondi (1991), permits the resolutions of
ambiguities in flight (on the fly, or OTF) without any initialization in static
phase, which would obviously not be possible.
The initialization of the ambiguities fixation in flight cannot be performed
beyond a distance of 10 km between the fixed receptor and the mobile.
Once the initialization is made, the basis can go until 30 km, but without
cycle slip. If there is a cycle slip, an OTF traditional software will do the
initialization again, and therefore the mobile receptor should come once
more closer than 10 km from the reference. This method of ambiguity
resolution in flight is widely used by numerous constructors and GPS users,
but it has the major inconvenience, in an application of photogrammetric
production, of imposing maximal lengths of bases of about 30 km. Some
constructors provide solutions for bases ranging to 50 km, but no full-size
test has been achieved again. Nevertheless, the order of magnitude remains
the same and requires the presence of a nearby fixed receptor on the zone
to photograph.
The GPS positions, calculated during the mission are those of the centre
of phase of the antenna. However, the position that interests us is that of
the perspective centre at the time of the image acquisition. It requires a
good synchronization between the image acquisition and the GPS receiver,
and a perfect knowledge of the vector antenna/camera at the time of the
image acquisition. This vector is constant in the airplane frame, on the
other hand it is not in the earth reference system. It is therefore necessary
to calculate the matrix of passage between the two systems, either using
ground points, or knowing the attitude of the plane at the time of the
image acquisition.
2.3.1.4 Measures of airplane attitude
Use of GPS in photogrammetry 117
The measure of attitude by GPS is an interferometric mode. One measures
times of arrival of the wave on a system of several antennas forming a
strong solid shape. It requires a perfect synchronization on times of arrival
to the different antennas. It is achieved with the use of receptors, a clock,
and several antennas. One finds currently on the market systems of three
or four antennas.
The more the antennas are separated from one another, the better is the
angular precision. Unfortunately, it is very difficult to get solid polygons on
planes used for aerial pictures, due to the flexibility of the wings (with the
notable exception of airplanes with high wings). The currently achievable

118 Thierry Duquesnoy et al.
precisions are in the order of the thousandth of a radian whereas a precision
ten to a hundred times superior would be necessary.
It is possible, but at a considerable cost, to couple to the GPS an inertial
system (IMU, for inertial measurement unit). The utilization of the
inertial system alone is not possible because it drifts very quickly. But then,
coupling the inertial platform with the GPS measures will cancel most of
the drifts, and makes it possible to get a precision on the angular measures
of about 10 5 radians. This is the device used in aerial laser scanning.
Information of attitude is known in real time in the plane and can therefore
also be used for the navigation in order to minimize overlap errors,
and to have a sufficiently precise assembly picture at the end of the aerial
mission.
2.3.1.5 GPS terminology
• Kinematics: differential method (DGPS) based on the measure of phase
of at least four satellites. The principle consists in solving the ambiguities
by an initialization, then to observe the points for a few seconds
while preserving the signal on satellites during the journeys, and therefore
the same integer ambiguities.
• Pseudo-kinematics: original method of kinematic type that consists of
reobserving the reference points and treating the file of observation as
if it was a fixed station having a gap in its data (ambiguities being
the same).
• Dynamic: differential method (DGPS) with observations of pseudodistances,
the station of reference whose coordinates are known, sends
by radio in real time the corrections to the mobile station, which may
then calculate its position.
• Trajectography: specific mode that uses observations of phase and
pseudo-distances, the computation being performed using pseudodistances
smoothed by the phase.
• Navigation: we will associate to this term the common sense of navigation,
that is the knowledge of information on the position and the
attitude of the plane that could allow the pilot as well as operators
to rectify their trajectory or the orientation of the camera in situations
requiring it.
2.3.2 Use of GPS in aerotriangulation
Yves Egels, Michel Kasser
2.3.2.1 How to limit the stereopreparation work
Whatever the photogrammetric product to be achieved (vectorial restitution,
orthophotography, DTM), it is indispensable to determine in a previous

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Use of GPS in photogrammetry 119
phase the formulas describing the geometry of the used pictures. This phase
is traditionally called aerotriangulation (or spatiotriangulation in the case
of spatial images, whose geometry is often different). We will recall quickly
here the principle of this classic method in analytic photogrammetry (one
will find the complete survey of this problem in any good book on analytic
photogrammetry), and we will develop only the improvements made
possible by the appearance of digital photogrammetry.
Let’s recall that the geometric properties of images alone do not permit
one to know either the position, or the orientation, or the scale of the
photographed objects. The determination of the corresponding mathematical
similitude cannot be obtained except by external measures: thus,
if one limits oneself to the case of the stereopair, and to determinations
of ground control points, it will be necessary to measure at least two points
in planimetry and three points in altimetry.
The aim of aerotriangulation is to reduce as much as possible this requirement
of field measures, by processing simultaneously the geometry of a
large number of images. The goal is to adjust (often to the least square
sense) the measures of coordinates in the images of the homologous tie
points, a certain number of ground points being considered as known, and
possibly auxiliary measures recorded during the photographic flight as well,
or satellite trajectography data. This leads generally to an overabundant
system of several thousands of non-linear equations, that one will be able
to solve by successive approximations from an approached solution.
Many software packages on the market allow one to perform this calculation.
Without any in-flight measures, they allow the necessary ground
points to be limited to one planimetric point for five to six couples, and
one altimetric point by couple. The digital photogrammetry did not bring
any basic difference at the level of the aerotriangulation calculation itself,
but on the other hand it allows the measure of tie points, which remained
manual (and very trying) in analytic plotting, to be automated almost
completely. Besides, the development of digital cameras, as they require
more images to cover a given zone, has led to the search for more efficient
auxiliary measures in order to restrict again the ground measures.
These normal mean values (one point in planimetry for five or six couples,
and one point in altimetry) depend in fact on the geometry of the work,
and in particular on overlaps from image to image (the minimal value is
60 per cent), as well as overlaps between neighbouring strips that have a
major impact in the rigidity brought to the general figure. If the overlap
between strips is significant (e.g. 60 per cent), every point is found in three
strips, but at the end it doesn’t permit an appreciable decrease in the
number of control points below half of values for a normal aerotriangulation.
On the other hand, one gets a much better reliability, and the
precision is improved as well.
This is a solution used for the survey of points that must be measured
with a very high precision, materialized by targets so that the pointing is

120 Thierry Duquesnoy et al.
almost ideal (e.g. measure of ground deformations). On the other hand,
the additional costs of this solution makes it a non-profitable one for classical
cartographic studies.
2.3.2.2 Use of complementary measures during the flight
One formerly used measures of APR (airborne profiles recorder, see §1.7),
a method that provided some vertical distances (radar or laser) from the
plane to the ground, with as altimetric reference an arbitrary isobar surface.
The airplane followed trajectories forming a grid, the points of impact
of the ranging unit to the ground being controlled by pictures acquired
by a camera. This methodology fell into obsolescence, but proved to be
quite useful to cover vast uninhabited zones (Australian desert, northern
Canada).
Use of complementary measures during photographic flights
It would ideally be necessary to know at each instant where a picture is
acquired:
• the position of the centre of the perspective, that is to say the optic
centre of the camera, in the reference frame of the work;
• the orientation of the camera.
These two groups of parameters are not at all equivalent in terms of necessary
acquisition expense.
For the position of the centre, let us note that almost no one uses the
differential barometer, which could bring some very interesting elements
while creating some strong new constraints on what is one of the major
weaknesses of aerotriangulation, that is to say the altimetry. This equipment
is otherwise functional without any external infrastructure, unlike
the GPS that we are going to examine, which is a more complete solution
on the other hand.
For the orientation of the camera, there does not exist a reliable and
low-priced sensor. The available inertial platforms are costly. Based on the
use of accelerometers whose values are integrated twice to get the displacements,
and on gyrometers or gyroscopes to measure the variations of
attitude, they have by their very nature a random drift more or less proportional
to the square of the time. This requires frequent updates, and this
updating can then be performed by the GPS. There are also (see §2.3.1)
some solutions using the GPS alone, measuring the GPS data simultaneously
acquired on three or four antennas. This is a mode that works like
the interferometry. Its angular sensitivity depends in fact on the antenna
spacing, the values of measure of the vertical component on each antenna
being hardly better than 1 cm. This implies, as the antennas cannot be

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Use of GPS in photogrammetry 121
more distant than 10 m (antennas on wings, the nose and the vertical
stabilizer of the plane) a precision of measure that is hardly better that
some millirad, with all the risks of GPS measures. By comparison, with a
pointing accuracy on image around 15 m (which is not excellent) and a
classic focal distance of 150 mm, one understands that the need in absolute
orientation is between 10 4 and 10 5 rad, which disqualifies de facto such
a use of the GPS. Otherwise, it would be necessary that the four antennas
form a rigid polyhedron, and it is not the case since most planes’ wings
bend according to constraints brought about by atmospheric turbulence:
the only noticeable exception is formed by planes with high wings, when
the implantation of antennas on wings is localized on the zone of shroud
grappling that holds the wings.
2.3.2.3 Positioning by GPS
The precision that it is necessary to achieve to localize the perspective
centres must be at least as good as that of points to localize on the ground,
and obviously depends on parameters of the image acquisition (scale, height
of flight, pixel size, etc.). In current cases it means a precision ranging
from 5 to 30 cm. We are in a dynamic regime, with a speed of the plane
around 100 to 200 m/s. It implies a very good synchronization between
the camera and the GPS receiver, which generally does not pose any particular
problem with the GPS equipment. The GPS should in this case have
a special input, the external events datation being performed with a precision
that reaches the 100 s level (GPS easily performs 100 times better).
But it is necessary that the camera provides a signal perfectly synchronous
(better than 0.1 ms) with the opening of the shutter, which is the case
with all modern cameras but is not always true of old equipment.
In addition it is necessary to get a continual positioning during the movement.
With GPS measures at each second, one has to interpolate the
position of the camera at the time of the signal of synchronization on
distances of 100 to 200 m, which does not permit a decimetric precision
as soon as the atmosphere is a little turbulent and creates perturbations
on the line of flight. And one should note that the higher the requested
precision, the more one flies at low altitudes and therefore the stronger
the turbulence. Thus a positioning adapted to large scales requires a better
temporal sampling than 1 s, a value of 0.1 s (yet rarely available on the
GPS receivers) being barely sufficient. In this optics, one can associate a
GPS receiver and an inertial platform that serve as a precise interpolator,
the bias of the inertial unit being small on one second, so that the unit
can provide data quite often (typically from 100 to 1000 Hz). But this
solution is quite expensive and still not very often used.
As we saw in §2.3.1, the precision requirements need the use of the GPS
in differential mode. Two modes can be used:

122 Thierry Duquesnoy et al.
• Kinematic mode, with measure of the phase on the signal carrier. Either
one initializes with a time duration permitting the ambiguity resolution
(it requires some minutes) and fixes them then for the remainder of
the flight. But then the reliability is low, and this is not used because
when the plane turns it frequently occurs that there are short
interruptions of the signal, ruptures in the continuity of the measure
that would oblige us to solve the ambiguities once more, which becomes
obviously impossible in flight. Either one solves ambiguities on the
flight (OTF, AROF, . . . methods), which overcomes this difficulty.
Nevertheless, it is necessary to note that up to now these methods work
only with reasonably short bases (20 or 30 km to the maximum), which
is poorly compatible with work conditions of photographic planes.
Indeed it would be necessary, before the beginning of the flight, to put
in operation a GPS station close to the zone to photograph. Risks of
photographic flight programming in the mid-latitude countries makes
such a step quite restrictive, the weather alone being a sufficiently strong
constraint not to add an obligation to set up such an equipment, which
would lead to too much time wasted. The only cases where one can
work according to this mode will be those where a permanent GPS station
close to the zone to photograph exist. This method is therefore not
very often used.
• Trajectography mode. One then measures the pseudo-distances as well
as the carrier phase. The precision is not so good, but one can work
with much more important distances to the reference station. We are
going to study this solution in more detail.
2.3.2.4 Survey of the trajectography mode
The satellite-receptor distance can be calculated on the one hand from the
time of flight of the wave deduced from the datation of the C/A code, the
clock correction, the tropospheric and ionospheric corrections (typical
precision of the order of one metre in differential mode). It can be calculated
on the other hand from the phase measurement, with an integer k
number of phase turns, from the correction of a clock, and from tropospheric
and ionospheric corrections (the precision is then millimetric, except
that k is unknown). The difference between these two variants of the same
distance being necessarily null in theory, while integrating measures on a
given satellite during enough time one can get an evaluation of k. This
mode is not adapted to real-time operations, on the other hand as long
as there are satellites in common visibility between the reference station
and the airplane, the result is usable as far as the GDOP (geometric dilution
of precision, a parameter giving an evaluation of the geometric quality
of the observable satellites, the smaller figures meaning the better geometry)
is correct, and the observed bases can range beyond a thousand
kilometres.

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Use of GPS in photogrammetry 123
Results are in general always of the same type: for a few minutes the
noise of determination of airplane coordinates is lower than 5 cm, and
one observes a bias, positioning errors varying slowly, with a typical time
constant of 1 or 2 hours, the amplitude of the errors being of the order
of one metre. This is due to the slow changes of satellite configuration in
the sky, the orbit errors being directly input in the calculations.
We may then model the GPS measures as an error of general translation
of the GPS positions for every applicable short temporal period,
typically of 10 min, for example for every set of photographs taken along
a given flight axis. One adds thus a supplementary unknown triplet in the
aerotriangulation for every strip. If one works in differential mode, the
precision is then centimetric, and in absolute mode this is without significance
since there are reference points on the ground that completely impose
the wanted translation for the whole set of images.
One thus succeeds in decreasing considerably the number of ground
points: in planimetry, it is necessary to get now at least 4 points by block,
and some more but only for controls, and in altimetry 1 point all 20 or
30 couples is satisfactory. These points don’t necessarily need to be to the
extreme borders of the zone.
One should be very attentive to problems that are linked to reference
frames. In particular in altimetry one should remember that the GPS
measures are merely geometric, whereas the levelling of reference is always
based on geopotential measures. Geoid slopes, or rather slopes of the null
altitude surface, must be taken into account according to the requested
precision.
One can consider treating the work without any ground references at
all (inaccessible zones for example). In this case one gets a coherent survey
but with a translation error of metric size, translation that is the mean
value of the systematism unknowns.
One should be also attentive to the geometry of the set of stereopreparation
points. If they are all reasonably aligned, the transverse tilt will be
undetermined. It is necessary to include points therefore in the lateral
overlap zones between strips. If one works on a zone without sufficient
equipment in levelling, one will be able to improve the quality of the aerotriangulation
by crossing the parallel strips by transverse photo strips. But
it will be necessary to perform levelling traverses on the ground if the
geoid slope is unknown, just to impose its slope in the geometric model.
2.3.2.5 Adjusting the link between the GPS antenna to the optic
centre of the camera
One will start with measuring with classical topometric methods the link
vector E ranging from the antenna to the optic centre, in the airplane reference
system. XA being the position of the antenna, XS that of the optic
centre, one will write:

124 Thierry Duquesnoy et al.
X S X A T R·E, (2.14)
where T is the vector describing the residual systematism of these measures,
and R describes the rotation of the airplane in the reference system of the
study, assumed equal to the rotation of the camera, itself even deduced
from the rotation of the bundle, a by-product of the collinearity equation.
2.3.2.6 Conclusion
The use of the GPS (or any other GNSS, like the Russian GlONASS or the
future European GALILEO) in the plane is a very important auxiliary source
of data to reduce the costs of the control points on the ground for the aerotriangulation.
But in such a case it is necessary to be aware of the imperfections
of the GPS, and to know what to do when some subsets of data
are not exploitable. On the other hand, it must be well understood that if
some inertial measurements may help considerably to interpolate within the
GPS data, they cannot correct its possible defects, and thus such data should
be considered as additional, every possible effort should be made to have
the best possible signal in the antenna: any device allowing the absolute
orientation of the camera to be provided will be welcome, but while waiting
for its availability, the GPS already gives excellent results . . .
Reference
Remondi B.W. (1991) Kinematicc GPS results without static initialization. NOAA
Technical Memorandum NO S NGS-55.
2.4 AUTOMATIZATION OF AEROTRIANGULATION
Franck Jung, Frank Fuchs, Didier Boldo
2.4.1 Introduction
2.4.1.1 Presentation
This section concerns the automatic determination of aerotriangulation. This
automation aims at the production of tie points and their use in two domains:
the aerotriangulation itself and the automatic realization of index maps,
which is a preliminary step to any aerotriangulation process. The reader will
note that we do not consider here the measure of the reference points. One
will not treat their determination (which is made by techniques of geodesy),
or the measure of their position in images (which are measured by hand).
The automatic calculation of tie points is a topic of growing interest
notably by reason of the increasing number of images produced for photo-

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Automatization of aerotriangulation 125
grammetric studies. In particular, both the use of digital cameras that is
now increasing, and of strong overlaps (notably interstrips) on the other
hand, generate images in greater number than in the past. It is henceforth
possible to find a substantial number of manufacturers of aerotriangulation
software proposing a module of automatic determination of tie points.
These modules are able to give good results on simple scenes (including
neither important relief nor too large-textured zones). However, the determination
of tie points in not so simple configurations still mobilizes greatly
the community of researchers. These less simple configurations are notably
terrestrial photogrammetric studies, aerial images of different dates, scenes
with strong relief, etc.
This type of problem is a topic of a working group on behalf of the
OEEPE (Organisation Européenne d’Études Photogrammetriques Expérimentales)
(Heipke, 1999).
2.4.1.2 Basic notions
We should recall some notions that will be used in what follows:
• Tie point: 3D coordinates often corresponding to the position of a
physical detail of the scene, and seen in at least two images.
• Measure: 2D coordinates of the projection of a point (of reference, or
of link) in an image.
• Point of interest: a point of the image around which the signal has
specific characteristics, such as high values of the derivatives in several
directions or at least two orthogonal directions, and detected by a
particular tool (e.g. detection of corners, of junction).
• Similarity measure: function associating to two neighbourhoods of two
points a real finite number. The more often used measure is the linear
correlation coefficient.
• Homologous points: set of points satisfying some properties in regard
to the similarity measure. Generally, a point P 1 of an image I 1 and a
point P 2 of an image I 2 are judged homologous if, for any P of I, P 1
and P 2 are more alike than P and P 2 , and for any Q of I 2 , P 1 and P 2
are more alike than P 1 and Q.
• Repeatability: quality of a detector of points of interest capable, for
a given scene, of detecting points of interest corresponding to the same
details in the different images, even if conditions of image acquisition
vary (lighting, point of view, scale, rotation . . .). A detector of points
of interest is more repeatable if it produces the same sets of points for
a given scene in spite of variations of the condition of image acquisition.
This notion is specified in Schmid (1996).
• Disparity: for two images possessing a weak rotation angle one in
relation to the other, the disparity of two points is the vector equal
to the difference of their coordinates. In the case of aerial image

126 Franck Jung et al.
acquisitions with vertical axis, the disparity of two points corresponding
to the same physical detail of the land is bound directly to
the altitude of this detail. This notion may be extended to the case of
images possessing any relative rotation.
2.4.2 Objectives of the selection of points of interest
This section discusses three points concerning objectives of methods of
automatic measurement of tie points. We will treat first their reliability,
then their precision, as well as a third important point, which makes an
important difference between the automatic measurement of tie points and
the manual techniques: it is about the number of tie points.
2.4.2.1 Reliability
Most methods of aerotriangulation depend on an optimization using a
least square adjustment technique. This technique is especially sensitive to
aberrant values. As usual it is therefore necessary, during the calculation
of tie points, to try not to provide any aberrant measures.
The first major objective toward a method of automatic measurement
of tie points is thus to provide points that are exempt from mistakes.
2.4.2.2 Precision
This second major objective can be the carrying out of complementary
studies as soon as one knows that the aerotriangulation work has been
performed correctly (i.e. there are no more mistakes).
To get a better precision for the aerotriangulation implies more precise
measures of tie points, but also taking into account in methods of aerotriangulation
an error model adapted to the real errors made by measuring
tools (which implies a study of these errors to model them correctly).
Indeed, error models used are generally Gaussian, and it remains to prove
that this model is suitable for a particular measuring tool. If necessary an
adaptation of the error model may be advisable.
2.4.2.3 Number of tie points
Traditional aerotriangulation uses 15 measures by image, whereas tools of
automatic measure of tie points are able to provide a large amount of data.
In the manual case, these points are very satisfying, because they are
selected by an operator. The operator can notably a priori assure their
geometric distribution. In the automatic case, the lack of intelligence of
any computer method may be partly compensated by the abundance of
data. Concerning the distribution of points, it is difficult to force the
machine to ‘find’ a solution in a given zone, and it is therefore probably

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preferable to let it find another solution in the neighbourhood of the desired
area. Concerning errors, the abundance of data does not reduce the error
rates of the methods, but permits the use of statistical tools aiming to eliminate
these errors.
Studies are not however advanced enough to permit one to fix an ideal
value of measures by image. Nevertheless, one expects that the number of
required points be appreciably higher in the automatic case (typically 100
measures by image (Heipke, 1998)). The debate on this question remains
very open.
2.4.3 Methods
Automatization of aerotriangulation 127
The automatic measurement of tie points generally requires two major
steps. The first concerns the detection and the localization of points of
interest in images. Points of interest can be calculated individually from
the images. Then these points are used to produce the actual tie points.
The passage of points of interest to tie points can be generally performed
with two opposite strategies.
In the two cases, strategies search between images for points whose value
of similarity measure used is maximal. Strategies differ according to the
zone in which one looks for the maximum.
For a point of interest P of an image I, the first strategy consists in
searching in an image J for the position of the point Q that maximizes
the value of similarity among all possible positions (all pixels of a region
where one expects to find Q). One can even consider calculating the position
of Q with a sub-pixel precision. This strategy, which one will call
‘radiometric’ is oriented: I does not play the same role as J in this case.
The second strategy consists in restricting the research space in J to only
the points of interest calculated. One will call this approach ‘geometric’
because it is focused on the position of tie points.
2.4.3.1 Methods of detection of points
Detectors of points use particular features of the signal. We will more
especially mention the detector of Förstner (Förstner and Gülch, 1987)
(much used in commercial software) as well as the detector of Harris whose
repeatability is high (Harris and Stephens, 1988; Schmid, 1996).
These detectors generally have a poor localization precision. Experiences
have shown a shift (rms) of 1 to 1.5 pixel between the real corners and
the detected points (Flandin, 1999). Nevertheless, the delocalization of
these points possesses a very strong systematism but a low standard
deviation (around 1 ⁄2 pixel). Thus it is possible to consider these points
as satisfactory for a photogrammetric set-up. A better localization of
these detected points can be considered by the use of specific techniques
(see §2.4.2.2).

128 Franck Jung et al.
Figure 2.4.1 Two 300 × 200 images and their points of interest.
Figure 2.4.1 represents two neighbouring images (size 300 × 200) with,
in white, their points of interest. Considering the density of points, their
representation is difficult and the visual inspection of the images must be
done carefully. Figure 2.4.2 shows matching points between these two
images. An attentive observation shows that the matching is quite often
correct. Obviously homologous points are in the overlap zones of the two
images. Figure 2.4.3 presents two excerpts of these images, allowing one
to see the details of the matching points in a small area of the images.

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Figure 2.4.2 Results of the matching.
Automatization of aerotriangulation 129
2.4.3.2 Calculations of homologous points
• Photometric aspect: a similarity criterion much used in many matching
techniques is the coefficient of correlation. This coefficient is calculated
on two imagettes. The advantage of this technique resides in its
ability to match two zones with similar grey levels. Nevertheless, it is
necessary to use perfectly oriented images (problem of images with
strong rotations).
• Signal aspect: a criterion based only on the local resemblance (photometric
criterion) is not always sufficient. Indeed, the correlation
within a homogeneous zone or along a contour remains a source of
ambiguity. A competing or complementary strategy consists in only

130 Franck Jung et al.
Figure 2.4.3 Excerpts of the images with homologous points.
matching the points possessing particular features of the signal (Harris
and Stephens, 1988; Förstner and Gülch, 1987).
A mixed approach takes full advantage of the two methods. The detection
of points is made according to features of the signal and the matching
is done according to a photometric criterion.
2.4.3.3 Reliability
Tools contributing to obtaining a good reliability of tie points are numerous:

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Automatization of aerotriangulation 131
• Repeatability of the detector: one preferably has to use a point detector
with a good repeatability. Examples are the detectors of Förstner
(Förstner and Gülch, 1987) and Harris (Harris and Stephens, 1988),
among which Schmid (1996) shows that Harris’s possesses the best
properties of repeatability.
• Multi-scale approach: this approach allows one to guide the research
of the homologous point in full resolution with the help of a reliable
prediction of the disparity on sub-sampled images. This approach
allows two problems to be solved: on the one hand the problems of
outliers error (one may limit the size of research zones voluntarily);
on the other hand this approach allows a limitation of the combinatories
of the problem of matching in full scale. One can note that the
introduction of a digital terrain model (DTM) can partially replace
the use of sub-sampled images to predict research zones at full scale.
• Multiplicity: a visual assessment of the quality of tie points permits
one to note that the percentage of erroneous tie points decreases
appreciably with the order of the point (number of images for which
the point is visible). There are nevertheless several ways to exploit this
observation. A very reliable way is to consider a multiple point as
valid if all associated measures are in total interconnection with regard
to the similarity function, i.e. if each pair of measures is validated by
a process of image by image matching. Figure 2.4.4 shows this mechanism:
every couple of points of this multiple link has been detected
as pairs of homologous points by the matching algorithm.
It is necessary to note that the points with a strong multiplicity are necessary
for the calculation of aerotriangulation.
Photogrammetric filtering
Forgetting any consideration of radiometric type, one can also use the
photogrammetric properties of tie points. Indeed, each of these points are
supposed to represent the same ground point. Therefore, all perspective
rays must cross in one point. Several methods can be proposed to use this
A
Image 1
B
Image 2
D
Image 4
C
Image 3
Figure 2.4.4 Example of multiple point of 4th order in total interconnection.

132 Franck Jung et al.
property. The first consists in attempting to set up every couple individually,
for example by the eight points algorithm (Hartley, 1997). Technically,
this algorithm calculates the fundamental matrix associated to a couple of
images. If one notes u and u′ the projective vectors representing, in the
reference of the image, two homologous points, the fundamental matrix
F is defined by: u′ T Fu 0. In return for some numeric precautions, the
algorithm permits the calculation of the likeliest fundamental matrix associated
to a sample of points. From the fundamental matrix, it is possible
to determine the epipolar line associated to a point u, and therefore also
to calculate the distance between u′, homologous of u, and this epipolar
line. This distance is a sort of ‘residual’ thus making it possible to qualify
points. This algorithm is very general, and permits a setting up of whatever
is the configuration. It has been used therefore for all sets of two
images having at least nine points in common, whatever their respective
positions. In this practice, for every ‘couple’ one attempts an iterative stake
in correspondence: one sets up, one calculates residues, one eliminates
points having a residual greater than three rms, and one repeats the setting
up, and this until this one is satisfactory, or the process is consolidated.
If the convergence could not have taken place, one then tries a stochastic
approach algorithm ([Zhang and Gang, 1996]): one chooses N samples of
tie points and applies the algorithm on every sample. Residues are then
calculated on the whole set of points, and one preserves the setting up
where the median of the residues is the weakest. If one of the methods
has given a satisfactory set-up, one eliminates all points whose residual is
greater than three times the median.
• If the number of exact points exceeds appreciably the number of errors,
the setting up is valid, and the points whose discrepancy with the
setting up is too high are eliminated. Another method is to really use
the photogrammetric knowledge. While doing an approached setting
up, errors appear. The only limitation is that most aerotriangulation
software are not intended to manage thousands of points automatically
generated by algorithms. Adapted tools must therefore be set up.
• On terminating filtering, one wishes to generally choose among the
remaining points, according to criteria like the distribution or the a
priori validity. Indeed, the distribution of points is not absolutely
uniform, some zones being over-equipped in comparison to others. In
order to limit this phenomenon, and to limit the number of points in
the aerotriangulation, it is necessary to choose among the set of filtered
points. Criteria to take into account are the equidistribution of points,
the a priori validity of these (in general, one can value the validity of
points during their calculation), in order to guarantee having some
exact points in every inter-images relation.

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Figure 2.4.5 (a) Examples of error sources (top: vehicle moving; bottom: areas
locally similar).
Figure 2.4.5 (b) Example of error source: textured zone.

134 Franck Jung et al.
Figure 2.4.5 (c) Example of correct point.
2.4.3.4 Precision
To obtain precise tie points, two main approaches exist. The first consists
in attempting to search for sub-pixel positions that maximize the function
of similarity. This technique looks mostly like optimization methods. The
important point concerning this method is that it links precision and resemblance:
the tool used to put the points in correspondence and to localize
them precisely is the same.
The second is more geometric, and decouples questions of resemblance
and precision. It aims at determining points corresponding to certain details
of the ground in a precise way, without trying to put them simultaneously
in correspondence (one will nevertheless note that the detection step is not
completely independent from the setting in correspondence step; one should
indeed preferably choose the points susceptible to being put easily into
correspondence, namely those points with good geometric behaviour, like
corners, crossings, etc.). A possible way consists in using the theoretical
models of corners or positioning points on intersections of contours determined
precisely. The putting into correspondence of these points will not
change their localization.
Generally speaking, the precision of localization of measure in images
depends on the algorithm used for the detection of tie points. The impact
of points of interest having a sub-pixel precision on the quality of the
aerotriangulation is still, to a very large measure, to be proven. The
matching aspect in this type of problem remains also very difficult. Subpixel
coordinates of the homologous points can be estimated separately,
or jointly during the phase of matching.
For this approach, one can mention the techniques based on theoretical
models of corners, or Blaszka and Deriche (1994), or Flandin (1999).

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Figure 2.4.6 Example of multiple point of 4th order.
2.4.3.5 Use of photogrammetry
Even though the problem stands upstream of aerotriangulation, photogrammetry
can constitute a considerable help in solving the problem of
the measurement of tie points.
Photogrammetry can guide methods (by a multi-scale approach) to
reduce the combinatories of the problem (by the prediction of homologous
positions at the time of the matching), and finally to filter the tie points
after their calculation, which contributes appreciably to their reliability.
2.4.4 Discussion
Automatization of aerotriangulation 135
The sections above have exposed some general considerations on objectives
and methods bound to the automatic measurement of tie points. We
have also to discuss limits and extensions of the existing processes. Indeed,
even though the existing systems give good results, there are many problematic
cases, as well as numerous possible extensions to less classic cases.
These problems may be analysed according to several axes intervening in
photogrammetric cases: the sensor, the scene, the image acquisition.
Finally, we will present some algorithmic considerations.

136 Franck Jung et al.
2.4.4.1 The sensor
Use of colour
A priori, the use of colour should allow for a better identification of ground
details, but currently it proves to be that most methods use mainly images
in grey levels, for the detection of points of interest and for the calculation
of tie points as well.
Quality of the signal
One expects a priori to get tie points of better quality with a sensor of
better properties: detectors of points of interest generally use the differential
properties of the signal; they are therefore sensitive to the image
noise. Thus, a better signal to noise ratio in images draws a better stability
from these operators. In practice, the evaluation of the sensitivity to the
sensor requires the use of important equipment, so as to perform flights
in identical conditions, so that no survey has been conducted on the question
up to now.
Multi-sensor data
The integration of multi-sensor data is a problem that will occur, because
one can consider embarking several cameras simultaneously for a flight
(for example, simultaneous embarking of sensors specialized by channel:
red, green, blue, and even infrared). No survey on this question and no
software dealing with this problem in an operational condition is currently
available.
2.4.4.2 The scene
Variation of the aspect of objects
The aspect of objects can vary according to the point of view. In the case
of a slope, the perspective distortions can be appreciable (the worse case
is facades in vertical aim). The occlusions are not the same. Finally, the
aspect can change according to the point of view. Figure 2.4.7 presents
two images of the same scene, obtained during the same flight, from two
different viewpoints. The superposition of the two images shows distinctly
the variations of intensity observed from these two points of view.
Forests, shades, textures
These objects generally create problems in image analysis. In the case of
the measure of tie points, they provoke three types of problems. Trees

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Automatization of aerotriangulation 137
Figure 2.4.7 Example of change of aspect according to the point of view.
cause problems of precision of pointing. Shades move between two image
acquisitions, notably between two strips (the interval of time between two
neighbouring images of two different strips can exceed 1 h), and therefore,
even though extremities of shades can seem easy to delineate, they
are not valid from a photogrammetric point of view (see Figure 2.4.8).
Textures naturally lead to problems of identification: it is easy to confuse
two very alike details in zones with repetitive motives, typically: passages
for pedestrians.
Relief
The relief provokes notable changes of scale and variations of disparity.
When looking for homologous points, the space of research is generally
larger. In this case, the utilization of photogrammetry on the under-sampled
images (multi-scale approach) can prove to be useful.
Case of terrestrial photogrammetry
In this case, often the hypothesis of a plane land (and horizontal) is no
longer valid. The space of disparities is more complex than in the aerial
case (in the aerial case, with little relief, two images of the same scene are
indeed nearly superimposable, which is not the case in terrestrial imagery).
Figure 2.4.9 presents the case of a terrestrial scene where a street axis is
parallel to the optic axis: distortions bound to the perspective are very
significant, as well as the disparities of points.

138 Franck Jung et al.
Figure 2.4.8 Example of shade point extremity.
Figure 2.4.9 Terrestrial image acquisition example: the perspective distortions can
be significant.
2.4.4.3 The image acquisition
Rotation of images
The interest in using images of any rotation is to achieve some diagonal
strips in photogrammetric blocks, which makes them more rigid. Otherwise,
if one tries to calculate two overlapping photogrammetric studies
simultaneously, the case of large rotations may occur. Techniques of matching
generally use linear correlation coefficients between stationary windows.

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In the case of known rotation between images, these can be sampled so
that these techniques work. In the case of unknown angle rotation, it is
necessary to adapt the methods. Invariants by rotation resemblance
measures have been developed: one can consider turning the imagettes
(Hsieh et al., 1997), or to consider measures relying directly on invariants
(Schmid, 1996).
Image acquisitions at various scales
In the case of image acquisitions of different scales, measures of resemblance
must also be adapted, because they don’t generally support strong
changes of scale. One however knows the scales of image acquisitions,
which reduces the problem. But even at known relative scales, the problem
is significant, because in order to compare two imagettes of two different
scales, it is necessary to adapt one of the signals. Otherwise, for example
for the positioning of points of interest, errors committed by the detectors
may be different between two scales.
Image acquisitions at different dates
If one wishes to process simultaneously some images taken at different
dates, it is necessary to be careful after the inversions of contrast that may
occur (notably by reason of different positions of the shades). In the same
way, the aspect of the vegetation can change. Considering the evolution
of the landscape, a certain number of topographic objects can undergo an
important radiometric evolution (ageing of roofs).
2.4.4.4 Algorithmic considerations
Automatization of aerotriangulation 139
Parametrage of methods
As in all processes of image analysis, the survey of the parameters must
be made in order to learn how to master the method and to know its
limits. One will for example aim at reducing the number of critical parameters:
one can easily replace a threshold level of a correlation coefficient
(that is generally very sensitive) by the introduction of the symmetrical
crossed correlation (see description of homologous points in §2.4.1.2).
Number of useful points by image
Studies have shown that there was no improvement to the result of aerotriangulation
by using more than 20 points by image (if the 20 points are
correct). In the case of automatic measure, it is necessary to have more
points to be able to reject reliably the aberrant points. The necessary point
number is therefore higher (see §2.4.2.3).

140 Franck Jung et al.
Evaluation
The assessment of the quality of tie points is based on the quality of the
aerotriangulation resulting from this setting up. A first criterion of quality
is the values of the residues (in microns or in pixels) of tie points. Another
technique consists in assigning values to the quality of tie points with the
help of reference ground points. These ground points can be calculated
with the help of a reliable aerotriangulation or with ground measures.
Combinative
At the time of the research of homologous points between two images,
one may a priori attempt to put in correspondence any point of the first
image, with any point of the second image. In this case, the combinative
of the problem is important. In the case of n images, the combinative
increases again. The combinative can be reduced strongly while restricting
correctly the space of research of points homologous of a given point.
A classical technique for it is the multi-scale approach: by doing first
some calculations at a reduced scale, one may predict the position of a
point to search for.
Another solution resides in the ‘geometric’ approach: if, for a given
research zone, one does consider as good candidates only the positions of
points of interest that are present, and not all pixels of the region, then
the combinative falls appreciably. However, this method rests entirely on
the repeatability of the detector of points of interest.
2.4.5 Automatic constitution of an index map
The objective of the constitution of an index map is to calculate 2D information
of position and orientation of images of the flight, permitting the
placing of all these images in the same reference mark of the plan, so that
the homologous details of several images are at the same position in this
common reference frame. For two images possessing an overlap, it is then
possible to appraise a change of reference frame permitting the forecasting
of the position of a homologous point to a given point p. Thus, the index
map, beyond its own utility, serves as a guide for the detection of multiple
tie points.
Images are treated after a strong sub-sampling. One considers a global
reference frame to the plane, common to all images. It is the reference of
the block. What one searches for is, for every image I, a similitude permitting
the passage of coordinates of a point of the plane (x B , y B ) expressed
in the reference of the block, to its position p(x, y) in the image. The
problem is treated strip by strip, then by an assembly of strips. Techniques
rely on the detection of points of interest in images, and on the calculation
of the relative 2D orientation of a couple of images whose relative
rotation is an angle close to 0.

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Automatization of aerotriangulation 141
Detection of points of interest
This part of the method includes two parameters: the standard deviation
of the Gaussian used for smoothing and derivations, and the size of the
calculation window associated to these processes.
Processing a couple of neighbouring images
One supposes that neighbouring images possess a relative rotation of angle
of nearly 0, and that because of the strong sub-sampling, the disparities
of homologous points of the two images are all similar. Two homologous
points can be put therefore in correspondence without the problem of rotation.
For two points of interest Pi of the image I, and Qj of the image J
one considers cij the coefficient of calculated linear correlation on a square
window centred on each point. Two points Pi and Qj are judged homologous
candidates if for Pi no point of J is more alike, and reciprocally.
Formally:
∀j′, c ij′ c ij, ∀i′, c i′j c ij . (2.15)
One thus gets couples of points candidates for the images I and J. In practice,
many aberrations are present. One operates therefore a filtering in
the space of disparities. For two homologous candidate points, one defines
the vector of disparity joining these two points. This is the vector obtained
by difference of coordinates of points. While accumulating these disparity
vectors in a histogram, one gets a cloud corresponding to the points of
similar disparities. These points constitute the homologous points retained
by the method.
In practice, the cloud is identified by a morphological closing with an
square structuring 3 × 3 element. After closing, the connex component of
the strongest weight is identified, then the points participating in this
component are selected. At this step one defines the performance of an
image couple: it is the ratio between the number of points participating
in the cloud of points and the number of homologous candidates points.
From these points one appraises with the least squares the likeness
allowing the best joining of the two references of the images. It permits
the second image to be put in the reference frame of the first. This part
of the method includes only one parameter concerning the correlation: it
is the size of the calculation window. The size of the structuring element
for filtering is otherwise stationary.
Process of a strip
One supposes one knows N images constituting a strip. The previous
process is applied to the N1 successive couples constituting a strip. One
can thus ‘sink’ all images of a strip in the reference of the first image of

142 Franck Jung et al.
this strip. All strips are treated independently. There is no supplementary
parameter concerning this step.
Process of a block
One supposes one knows the order of strips. One also supposes that strips
possess a correct lateral overlap (> 10 per cent). This part of the method
is achieved by iterations: one glues the strip n 1 to the organized block
of the n previous strips. One considers therefore that one already has a
block organized to which one adds a supplementary strip. It is achieved
while first hanging an image of the strip to the block, then hanging up
the other images of the strip, image by image.
• To hang up an image of the strip to the block: for an image I of the
strip, one temporarily considers all couples between the images I and
J of the last strip of the block. One also considers couples between
the images I and J having undergone a rotation of . For all formed
couples, one performs the process of image couples studied earlier,
then one keeps the couple possessing the best performance. If this
performance is not sufficient, one repeats the operation until one finds
an effective enough couple. One thus gets a couple in an image I 0 and
J 0 permitting the image I 0 to be put in the reference frame of the block.
• Progressively one sinks images of the strip in the reference of the
couple. To avoid error accumulations, an optimization of the system
is done at regular intervals (every n opt images), by a method described
in the following.
This part of the method introduces two parameters. The first is the
threshold of performance beyond which one accepts the coupling of image
between the strip and the block. This threshold is fixed to a value that a
precise survey showed was quite reliable. The second is n opt 5. This
value allows the method to be reliable while reducing the number of optimizations.
Optimization of block
This optimization aims at refining the positions and orientations of the
images of a block. This is necessary because it is not possible of ‘to glue’
in a rigid way two strips because of distortions that accumulate at the
time of the constitution of the intra-strip index map. One considers all
couples of images possessing an overlap. For each couple, the homologous
points to the previous sense are calculated. A function of cost aiming to
achieve the objective of the image assembly is minimized. Technically this
function is the sum of cost functions bound to every couple of images.
The function bound to a couple of images aims to minimize, for each of

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Automatization of aerotriangulation 143
the homologous points of the image couple, the distance of the two homologous
in the reference of the assemblage image. This function is adjusted
so as to avoid the aberrant points.
Survey of parameters for the constitution of the index map
The behaviour of parameters is known. It appears notably that for some
among them, values are stationary in the sense where meaningful studies
have been processed without modification. These are:
• the value of the standard deviation of the Gaussian in the calculation
of points of interest, as well as the size of the associated calculation
window;
• the size of the correlation window for the calculation of homologous
candidates points;
• the size of the structuring element used in filtering in the space of
disparities.
For the other parameters, their behaviour is known: their variation allows
an increase in reliability at the cost of more calculation time in any case,
or inversely. In this sense, the sensibility of the parameters is low as their
influence on the results is identified.
Figure 2.4.10 Excerpt of an index map (city of Rennes, digital camera of IGN-F).
14 strips of 60 to 65 images. The geometric precision of
mosaicking is good: the errors on the links range to 1 or 2 pixels.

144 Franck Jung et al.
2.4.6 Conclusion
The problem remains wide open. Nevertheless, under certain conditions,
some systems are quite capable of producing tie points adapted to calculate
photogrammetric works. These tools can be very useful for large
studies.
In any case, digital photogrammetry will need such tools, which justifies
completely the ongoing developments in this domain: the problematic
zones (occlusions, strong relief, texture, change of date, strong scale variation,
etc.) remain difficult points for these methods.
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relative 3D de images. Stage Report, Institut Géographique National France.
Förstner W., Gülch E. (1987) A fast operator for detection and precise location
of distinct point, corners and centre of circular features. Proceedings of the
Intercommission of the International Society for Photogrammetry and Remote
Sensing, Interlaken, Switzerland, pp. 281–305.
Harris C., Stephens M. (1988) A combined edge and corner detector. Proceedings
of the 4th Alvey Conference, Manchester, pp. 147–151.
Hartley R.I. (1997) In defense of the Eight-Point Algorithm. IEEE Transactions
on pattern analysis and machine intelligence, vol. 19, no. 6, June, pp. 580–593.
Heipke C. (1998) Performance of tie-point extraction in automatic aerial triangulation.
OEEPE Official publication, no. 35, pp. 125–185.
Heipke C. (1999) Automatic aerial triangulation: results of the OEEPE-ISPRS test
and current developments. Proceedings of Photogrammetric Week, Institute for
Photogrammetry, Stuttgart, pp. 177–191.
Hsieh J.W., Liao H.Y.M., Fan K.C., Ko M.T., Hung Y.P. (1997) Image registration
using a new edge based approach. Computer Vision and Image Understanding,
vol. 67, pp. 112–130.
Schmid C. (1996) Appariement d’images par invariants locaux de niveaux de gris.
Thèse de doctorat de l’institut National Polytechnique de Grenoble.
Zhengyou Zhang, Gang Xu (1996) Epipolar Geometry in Stereo, Motion and
Object Recognition. Kluwer Academic Publishers, pp. 102–105.

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Digital photogrammetric workstations 145
2.5 DIGITAL PHOTOGRAMMETRIC WORKSTATIONS
Raphaële Heno, Yves Egels
2.5.1 Introduction: the functions of a photogrammetric
restitution device
Whatever its principle of realization, one will find in any photogrammetric
restitutor a certain number of basic functions that one can represent on a
working diagram (Figure 2.5.1). This principle of working was discovered
during the first industrial realizations at the beginning of the twentieth
century (restitutor of Von Orel at Zeiss, Autograph of Wild). In the
first systems, the geometric function is achieved by an optic or mechanical
analogue computer (whence their ‘analogical restitutors’ name). The
two other functions use a human operator, whose stereoscopic vision
assures the image matching, and whose cultural knowledge the interpretation.
In the 1970s, a first appreciable evolution appeared, the analytic restitutor:
image formulas are calculated analytically by a computer, which
displaces images from an optic system using a servo, because images being
Movement
Input
peripheral
No
No
Left image
formula
Field
x, y, z
Right image
formula
Left x, y Right x, y
Are the
points
homologous?
Yes
Is
the point
interesting?
Record of the point (GIS)
Figure 2.5.1 Schematic diagram of the photogrammetric restitution.
Yes
Geometry
Correlation
Interpretation

146 Raphaële Heno and Yves Egels
on films, the matching as well as the interpretation are always done by a
human operator.
Today, images become digital, and can be visualized on a simple
computer screen. Besides, non-geometric functions are more often taken
into account by algorithmic means, and the human operator, and therefore
the visualization itself, then becomes superfluous. In this last case,
there isn’t a photogrammetric restitutor strictly speaking, but only a specialized
software functioning on more or less powerful computers.
In the following, one is concerned mainly with the case where a human
operator must, instead of achieving the totality of photogrammetric process
by hand, at least supervise it, control its results, and possibly perform
certain operations by hand.
2.5.2 The technology
2.5.2.1 The equipment
The passage to the digital in photogrammetry allowed a freedom from the
high-precision optic and mechanical components, which kept the acquisition
and maintenance costs of systems at a very high level. In addition,
the size of the machines was considerably reduced (see Figure 2.5.2).
Systems of digital photogrammetry are based on workstations or, increasingly,
on PCs. The recent computers include almost the whole of the
necessary means for photogrammetric restitution, and today have enough
power for these applications. Nevertheless it is necessary not to forget
that the manipulated data images generally have sizes of several hundreds
of megabytes, and that a given study will require the use of tens, or even
hundreds of images. The capacity of storage, and access times, should
therefore be especially adapted.
Only two indispensable elements are not yet completely standard, even
if the development of video games makes them more and more frequent:
the peripheral for data input and the stereoscopic visualization; as regards
the computer conception, digital photogrammetry is hardly more than a
video game with a technical aim.
Peripheral for data input
The system must possess a peripheral of coordinate input able to address
three independent axes. Solutions are numerous, from arrows on the keyboard,
to the cranks and pedal of traditional photogrammetric devices, or
controllers of immersion of virtual-reality stations, joysticks, or the specialized
mouse. Only the cost/ergonomics ratio can overrule them. The practice
establishes that the movement must be as continuous as possible, and
that the control in position is far preferable to speed commands (joysticks).
When a specialized peripheral is developed, supplementary buttons may be

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Digital photogrammetric workstations 147
usefully attached, allowing one to simplify the use of the most frequent
commands.
Stereoscopic visualization
The system must also allow stereoscopic vision, inasmuch as one will ask
the operator to achieve some visual image matching. Here also, several
solutions exist, and some are under normalization. It is about presenting
to each eye the image he has to observe. In order of increasing comfort,
one can mention:
• the display of the two images in two separated windows, which the
operator will observe with an adequate optic system of stereoscopic
type, placed before the screen;
• the simultaneous display of the two images, one in green, the other
in red, the operator benefiting from the structural complementarity of
such glasses (anaglyphs) whose cost is extremely low;
• the alternative display of the two images, a device using liquid crystals
letting the image pass toward the eye to which it is destined.
In the professional systems, only this last solution is used, due to its better
ergonomics. The frequency of the screen conditions the quality of the
stereoscopic visualization, because the alternative display divides by two
the frequency really discerned by the user (a minimal frequency of 120
Hz is necessary to avoid operator fatigue). Several convenient realizations
are susceptible of being used. The liquid crystals may be placed directly
before the eye, a low-cost solution, synchronized by a wire or by infrared
link. Or they may be placed on the screen, the operator then using a couple
of passive polarized glasses (which allows him or her to look indifferently
Control screen
Cranks and
pedal
commands
Stereo display
Figure 2.5.2 Diagram of a digital photogrammetry system.
Hard disks
Central unit

148 Raphaële Heno and Yves Egels
at the stereoscopic screen and at the command screen), the most comfortable
solution but also the most expensive.
2.5.2.2 Photogrammetric algorithms
It was not necessary to reinvent photogrammetry to make it digital. The
equations are the same as those on the analytic photogrammetry systems
(equations of collinearity or coplanarity).
More and more systems are ‘multi-sensor’, that is to say that they can
not only process aerial images, but also different geometry images, for
example the images from scanning sensors or from radar. The setting up
of these images uses mathematical models different from the traditional
photographic perspective, possibly parametrable by the user.
Whatever their origin, once images are set up or georeferenced, the function
‘terrain → image’ allows one to transmit in real time the displacement
terrain introduced with the mouse or the cranks.
On the other hand, contrary to the analogical or analytic restitutors,
the availability of the image under digital shape allows a considerable
spread of the possibilities of the automation of photogrammetry, requiring
to bring together in one unique system photogrammetric functions and
functions of image processing and shape recognition.
2.5.3 The display of image and vector data
2.5.3.1 Display of images
The used images always have some sizes much greater than the dimension
of the screen (often 100 times larger). It will thus be necessary to be able
to displace the display window conveniently within the total image. Two
modes of displacement are possible: either the image is fixed, and the cursor
of measure mobile; or the cursor is fixed and central, and the image is
mobile. The measure will be performed by superimposing a pointing index
(whose colour will be adjusted automatically to the background image).
The image is fixed
The fixed image/mobile cursor configuration is easiest to implement: it is
just a question of displacing some octets in the video memory. But the
ergonomics of this solution is mediocre. If images are not reprocessed
geometrically (epipolar resampling), the transverse parallax is eliminated
in only one point, generally the centre of the image. During the displacements
of the cursor, some parallax appears, which makes the pointing if
not impossible, at least imprecise. Besides, when the cursor reaches the
side of the screen, the system must reload another zone of images, which
interrupts the work of restitution and distracts the operator.

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Digital photogrammetric workstations 149
The cursor is fixed
More demanding in calculation capacities, the mobile image/central cursor
configuration is far more preferable. If the displacement of images is fluid
enough, and it must be so not to tire the operator, this configuration recalls
the analytic devices, where image-holders move in a continuous way in
front of a fixed mark. Images are generally charged in memory by tiles,
to optimize the time of reloading.
The system sometimes proposes a global view (under-sampled image)
for the fast displacements in the model.
In the ‘exploitation of the model’ mode, it is preferable to dedicate the
maximum surface of the stereo screen to the display of the two images.
But then, at the time of aerotriangulation points measurement, it is convenient
to be able to display for every point all images where it is present
(multi-window).
2.5.3.2 Zooms and subpixel displacement
Zooms by bilinear interpolation, or to the nearest neighbour, serve to
enlarge all or part of the current screen. Their goal is usually to allow to
point with a better precision than the real pixel of the image. Unfortunately,
the zoom decreases the field of observation simultaneously and adds a
significant fuzziness to the image, these two effects degrading appreciably
the quality of the interpretation. Subpixel displacement of the image allows
these two defects to be palliated simultaneously (but this function is not
generally available in the standard graphic libraries, and requires a specific
programming).
In the case where the image is fixed, it is enough to resample the cursor
so that it appears positioned between two pixels, which requires that it is
1/1
Figure 2.5.3 Rear zoom pyramid.
1/2
1/4
1/16
1/8
1/32

150 Raphaële Heno and Yves Egels
even-formed of several pixels. If the image is mobile, then it is the totality
of the displayed image that it is necessary to recompute.
Concerning the rear zooms, they are immediately calculated or generated
in advance under the shape of a pyramid of physical images of
decreasing resolution (see Figure 2.5.3). In the case of image pyramids,
one won’t be able to zoom back at any scale.
2.5.3.3 Image processing
Within basic tools one finds at least the functionalities of adjustment of
the contrast, the brightness, of positive/negative inversion. Based on the
colour table (LUT, a term that stands for look-up table) of images, they
work in real time, and don’t require the creation of new images.
It is sometimes possible to apply convolution filters (contours improvement,
smoothing . . .). Their application being quite demanding for the
CPU, it slows down considerably the time required for image loading.
Besides, these filters often have some perverse effects on the geometric plan
(displacement of the contours), and the influence on the precision of the
survey can be catastrophic. For a better efficiency, one will prefer sometimes
to calculate new images.
2.5.3.4 Epipolar resampling
The visualization of a stereoscopic model whose images have been acquired
with appreciably different angles can be tedious for operators, because the
two images have too different scales and orientations. Performances of
usual image-matching techniques are degraded also by this type of images.
(See Figure 2.5.4.)
In this case, it is desirable to make an epipolar resampling: one calculates
the homographic plane that allows one to pass from the initial image
Image acquisition Left image Right image
Object Homologous
object
Figure 2.5.4 Visualization of stereoscopic model using images with significant
differential rotations.

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Images resampled in epipolar geometry
Digital photogrammetric workstations 151
Object Homologous
object
Epipolar lines
Figure 2.5.5 Epipolar resampling.
Plane containing
the basis
to the one that would have been obtained if optical axes of photos had
been parallel between them and perpendicular to the basis (normal case);
after this process, two points of a line of the left image will have their
counterparts in one line of the right image, and the transverse parallax is
constant. Epipolar lines are the intersections of the bundle of planes
containing the basis and of the two image planes. In the resampled images,
these lines are parallel, whereas they were converging in the initial images.
(See Figure 2.5.5.)
This resampling requires at least the calculation of the relative orientation
(and of course cannot be used at the same time as the measures
necessary for setting it up). It generates two new images, which must be

152 Raphaële Heno and Yves Egels
taken into account in the management of the disk space. As it is valid for
only one couple, it is possible to cut up images and to keep only the
common parts of images of the model.
Epipolar resampling not only improves the operator’s comfort, but it
accelerates the work of correlators, since the zone of research of the homologous
points is reduced to a one-dimensional space (instead of a twodimensional
space for a systematic correlation of images). Some systems of
digital photogrammetry require working with images in epipolar geometry
for the extraction of the DTM; others do this resampling continuously.
2.5.3.5 Display of the vectors
Whereas on the analytic restitutors the addition of a vector display on
the images (very useful for cartographic updating) was a very costly
option, requiring complex optical adaptations, the superposition of vectors
in colour to the images in stereo doesn’t pose any problem for digital
photogrammetry systems.
2.5.4 Functionalities
Digital restitution systems offer at least the same functionalities as the analytic
restitutors. Besides, these can practically be reused without change,
except for the addition of functions to help pointing, which profit from the
digital nature of the image. But their features allow one to consider numerous
extensions of their use. We summarize here the main among them.
Contrary to what happened in analogical or analytic systems, the
geometric quality of the products calculated on the digital photogrammetry
system (vector data base, DTM, orthophotos) will be reasonably
independent of the system. The geometric algorithms used are very close,
and no mechanics intervenes. The only difference lies in the pointing capability
which may be at the pixel level, or using sub-pixel methods. One
should especially be concerned with the quality of the following steps:
• condition of the films;
• quality of the digitization (type of scanner used, control of the parameters,
scanner resolution);
• quality of the control points;
• quality of measures of points of relative and absolute orientation.
2.5.4.1 The management of data
The manipulated images
Digital photogrammetry workstations are capable of working with images
originating from scanned classic aerial pictures, scanned terrestrial images,

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Digital photogrammetric workstations 153
or with the images of aerial or spatial digital cameras (e.g. the CCD matrix
digital camera of the IGN-F, the DMC of Zeiss Intergraph, the APS 40
of Leica Helava Systems, see §1.5).
The black and white 8 bits and colour 24 bits images are easily read
by digital photogrammetry systems. Considering that the images may have
12 bits or more by channel that are meaningful for the digital sensors, it
happens that only the first 8 bits of every pixel are used. Anyway, the
current computer screens actually display 6 bits only, which is also the
true dynamics of movies, and the human eye only distinguishes a part of
the 256 levels of grey of a coded image on 8 bits, but with the large
dynamics digital sensors, this loss of information is prejudicial for algorithms
of image matching and automatic shape recognition.
There is no consensus within manufacturers of digital photogrammetry
systems on the computer format of images to use. Nearly all are capable
of reading and writing the TIF (tiled or not), but some recommend
converting it to a proprietary format to optimize process times. It is the
same for the JPEG compression: its direct utilization slows down some
applications, as this technique (in its present state) prevents the direct
access to portions of image. The wavelet compression gives excellent results
in terms of the ratio ‘quality of compressed image/reduction of volume’,
and it is likely that the digital photogrammetry systems will quickly adopt
this process.
Photogrammetric database
The data necessary to important studies exploitation are quite numerous
and voluminous; they require a rigorous organization that is taken into
account, either by a hierarchy predefined by directories, or by a specific
database.
Systems generally allow one to store data by project, that correspond
intuitively to a given geographical zone, to a theme, etc. A project can
correspond to a directory of the arborescence of the system, in which one
finds the files necessary for setting up the models (files of camera, files
containing reference points, possibly files containing the measures on the
image achieved on another device . . .), as well as files generated by calculations
(parameters of the internal orientation, position and attitudes of
the camera for each of the cliches, matrixes of rotation . . .). Data are
managed by model, or image by image (a file by model, or a file by image).
Images are stored in this same directory, or, for convenience in the management
of the disk’s space, merely referenced there. (See Figure 2.5.6.)
The local networks (Ethernet 100, then Giga Ethernet) allow work in
architecture on a customer-server basis: images are set up and stored on
a machine ‘server’, while machines’ ‘customers’ use them (visualization,
process, survey) via the network, which requires mechanisms of control
of the data consistency.

154 Raphaële Heno and Yves Egels
Data in input
Data in output
images
2.5.4.2 Basic photogrammetric functionalities
Setting up of a stereoscopic couple
INTERNAL ORIENTATION
project
101.img
103.img
105.img
107.img
Camera.fil
Reference.fil
101 – 103.fil
103 – 105.fil
105 – 107.fil
Possible content
Figure 2.5.6 Example of photogrammetric database.
• Directory of model images
• Operator parameters
• Focus
• Parameters of the internal orientation for each
image
• Position of the camera for each image
ω, φ, κ, X, Y, Z
The internal orientation phase is always necessary for images coming from
a digitized classic aerial photograph. Knowledge of the theoretical position
of reference marks on the bottom plate of the camera (via the certificate
of calibration of the camera) and the shape of these reference marks allowed
at least a partial automation of this phase of measures, thanks to image
matching.
The operator is sometimes asked to search by hand for the first reference
marks, the system recognizing the next ones automatically. Automatic
image matching, if necessary, assists interactive pointing.
The internal orientation is completely automatic on certain systems.

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EXTERNAL ORIENTATION
Most systems calculate the relative and absolute orientations by the simultaneous
use of the collinearity equation. Even though the measure of points
of relative orientation is assisted by image matching, or even completely
automatic in cases where one uses a theoretical distribution of points, it
is always imperative that an operator marks by hand the position of reference
points.
The elimination of the parallax in X and in Y is generally performed
by blocking one of the two images, and by moving the other with the
positioning system (cranks, mouse). Once the choice of the fixed image is
made, one can ask for a pointing by image matching. In certain cases, this
one can fail (vegetation, periodic textures, homogeneous zones); the use
of the image matching does not dispense with a pointing by the operator,
even if it is not so precise, because it remains more reliable in spite of
everything.
As soon as enough points are measured (six points to have residues of
relative orientation, three ground points), one can launch a first calculation.
Then the function ‘ground → image’ is known, and allows one to
move automatically, for example on a supplementary control point. When
measures are sufficiently overabundant, the examination of calculation
residues allows one to control the quality of the setting up, and to validate
it.
Measures and acquisition in a stereoscopic couple
The acquisition is very often limited to a stereoscopic couple; the automatic
loading of images of the neighbouring couple on the edge of the
image is sometimes possible, but of course requires having all images
concerned already loaded on the device.
Basic functionalities of the digital photogrammetric system are:
• acquisition of points, lines, surfaces;
• destruction, edition of these structures.
Digital photogrammetric workstations 155
Ideally, the digital photogrammetric system is interfaced with a GIS that
manages data acquisitions in a database.
All functionalities of the GIS (spatial analyses, requests, multi-scale
cartography) are then directly usable after the data acquisition. Data are
structured according to a more elaborate topology (line, spaghetti, sharing
of geometry, object structure).
Data extracted from the digital restitutors are systematically tridimensional.
But rare are yet the GIS that allow one to manage completely a ‘true
3D’ topology (management of vertical faces, of overhangs, of clearings),
and not only of the 2.5D (planar topology, only one Z attribute by point).

156 Raphaële Heno and Yves Egels
The GIS generally propose interfaces toward the most current formats
(DXF, DGN, Edigeo . . .).
2.5.4.3 Advanced photogrammetric functionalities
Aerotriangulation
Aerotriangulation allows one to georeference simultaneously all images of
a site, using as much as possible the overlaps that they have in common,
with a minimum number of reference points. This operation starts with a
phase of measure of the image coordinates of a certain number of points
seen on the largest number possible of images. Then a calculation in block
allows one to determine the set of photogrammetric parameters of the
work. The modules of available aerotriangulation calculation on systems
of digital photogrammetry use the same formulas as the analytic aerotriangulation,
and are most of the time identical.
The measure of reference points, always interactive, is helped by the
multi-windowing: once a point is measured on a image, the system can
display in mini-windows all images susceptible of containing it, directly
zoomed on the zone concerned. This is made possible by the a priori
knowledge of the overlaps between images and their position in relation
to each other, determined by GPS, or via the assembly table defined by
the operator. The only work remaining for him is to measure the point
position in the window in which it is present, in monoscopy or in stereoscopy
as well, or with the assistance of an automatic image matching
process.
On another hand the measure of tie points is very automated: one can
replace the precise measurement done by a human operator by automatic
image-matching measures in very large number, either by the operator’s
choice helped by the multi-windowing, or by automatic selection of tie
points by an adequate algorithm. After filtering the wrong points, enough
points normally remain to assure the stability of the block.
Altimetry and digital terrain models (DTM)
The DTM can be used either as supporting data to the restitution, or as
a product. In addition, the digital photogrammetric workstations are
perfectly adapted to the control and the correction of DTM obtained by
automatic methods.
In the case where a DTM pre-exists (result of a previous restitution, of
a conversion of level lines . . .), it is possible to fix the measure mark to
the DTM, which frees the operator from a tedious task. However, this
help is quite limited, not only because of the frequently excessive generalization
of the available models, and of the non-representation of the
objects over the ground.

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Digital photogrammetric workstations 157
In an intermediate way, it is possible to help the restitutor thanks to a
real-time correlator, which replaces altimetric pointing. One uses in this
case a correlator working in the object space, fixing the altitude to the
maximum of the image matching detected on the vertical determined by
the system of command. But the correlator must be considered as a help,
and up to now it may work only in a supervised mode: many false correlations
may happen, especially when the signal/noise ratio is low, or for
example on specific periodic structures.
The complete make-up of a DTM is usually let to a non-interactive
process, possibly guided by some initial manual measures; indeed, the manual
acquisition of a DTM is a long and very trying operation. One prefers
to limit the human interventions to the control and the correction. The control
is often performed visually, essentially by stereoscopic observation of
level lines calculated from the DTM superimposed onto the couple of
images. For corrections, each worker imagined some different solutions,
from the local recalculation with different parameters, with possible integration
of complementary human pointings, up to more brutal operations
on altitudes themselves: new acquisition, levelling, digging, interpolation.
Aids to the interpretation
The functionalities of automatic or at least semi-automatic data extraction
are awaited with impatience by users, who invested in systems of digital
photogrammetry while hoping that algorithms of researchers would allow
them to quickly improve their efficiency. But with the exception of automatic
extraction of the DTM, and the cartographic restitution of contour lines, no
tool is yet industrially implemented on systems of digital photogrammetry.
Orthophotographies, perspective views
Digital photogrammetric stations are often seen as machines to manufacture
orthophotos. But actually, with the exception of the preparatory phases
(reference points of the aerotriangulation, control and correction of the
DTM) presented in the previous paragraph, it would be more economic
to use a specialized software functioning on a standard computer.
2.5.4.4 Limitations
Photogrammetric workstations allow one, fundamentally, to perform at least
the same work as analytic restitution devices, which they are progressively
going to replace. Nevertheless, it is certain that the ocular comfort of operators
is not equivalent to that of their predecessors, far from it. But as these
materials directly follow the possibilities offered by the PC for video games,
where the problem is quite similar, one can expect improvements of visual
comfort, a point that employers are more and more obliged to take into
account.

158 Raphaële Heno and Yves Egels
In addition, these stations allow processes otherwise impossible to make
on the same workstation, such as the realization of orthophotographies.
Let us note finally that these stations obviously require images under
digital shape, that are provided at present especially by digitization of
argentic images, which implies a phase of quite expensive digitalization
work currently, and a significant supplementary delay. The generalization
of the use of digital cameras providing directly digital aerial images will
make this situation evolve. In the intermediate situation that prevails to
the date of writing of this work, it is essentially the price of acquisition
and maintenance of equipment (that are hardly more powerful than simple
PCs) and of software (that democratize themselves considerably) that make
these stations attractive.

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3 Generation of digital terrain
and surface models
INTRODUCTION
The mathematic modelling of a landscape is a very important step of the
photogrammetric processes. It has several key applications, and among
them the cartography of the intervisibility (use of digital models for telecommunications,
cellular phones for example), the hydrologic studies, the
preparation of cartographic features (the contour lines), and the preparation
of orthophotographies. Thus we shall review some important points
that are not, strictly speaking, bound to the digital aspect of the photogrammetry
itself, but that in fact are such a substantial output of today’s
photogrammetry that it is necessary to analyse them here as completely
as possible. We will see how are defined and specified the various surface
models (§§3.1 and 3.2), how the data samples are produced (§3.3), how
to remove raised structures when one wants to get a DTM (§3.4), how
to build an optimal triangulation of a digital model so as to describe a
surface in the best way possible (§3.5), how to extract automatically the
characteristic terrain lines, as these lines are necessary to minimize
unpleasant artefacts of any DTM, particularly for hydrologic matters
(§3.6). Then we will conclude by some definitions, some quality considerations
and some practical remarks about the production of digital
orthophotographies (§§3.7, 3.8 and 3.9).
3.1 OVERVIEW OF DIGITAL SURFACE MODELS
Nicolas Paparoditis, Laurent Polidori
3.1.1 DSM, DEM, DTM definitions
A digital elevation model (DEM) is a digital and mathematical representation
of an existing or virtual object and its environment, e.g. terrain
undulations within a selected area. DEM is a generic concept that may
refer to elevation of ground but also to any layer above the ground such

160 Nicolas Paparoditis and Laurent Polidori
as canopy or buildings. When the information is limited to ground elevation,
the DEM is called a digital terrain model (DTM) and provides
information about the elevation of any point on ground or water surface.
When the information contains the highest elevation of each point, coming
from ground or above ground area, the DEM is called the digital surface
model or DSM.
Natural landscapes are too complex to be analytically modelled, so that
the information is most often made of samples. Theoretically, a genuine
‘model’ should also include an interpolation law that would give access
to any elevation value between the samples, but this is generally left to
the end user.
Together with the elevation data, the specification of a DEM is provided
by ancillary data. The specification, which is a description of the data set,
is necessary to let users access, transmit or analyse the data. It consists of
a number of characteristics that may be given as requirements.
3.1.2 DEM specification
The specification of a DEM generally includes two kinds of parameters.
On the one hand standard altimetric specifications do not differ from
the case of analogue maps, typically geodetic parameters (ellipsoid, projection,
elevation origin . . .) and geographic location (e.g. coordinates of
corners) but not scale, which is meaningless in the case of digital maps.
On the other hand, a DEM is a digital product that cannot lead to an
altimetric grid without a few specifications:
• the digital format, i.e. a type (integer, character, real . . .) and length
(often 2 bytes);
• the significance of numerical values, i.e. unit (metre or foot) and in
some cases, the coefficients of a conversion law, for instance a linear
transform that makes the values fit a specified interval;
• the grid structure, which may be irregular (e.g. triangular irregular
networks or digitized contour lines) or regular (typically a square mesh
regular grid);
• the mesh size, which is important in the case of a square mesh regular
grid – not to be considered as a resolution.
The impact these specifications may have on the quality of the DEM is
discussed in §3.2.
The three main widespread models are regular raster grids, triangular
or planar faces irregular networks, and iso-contour and break lines
networks.

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3.1.3 Digital models representation
3.1.3.1 Regular raster grid (RG)
Regular raster grids are well adapted to the representation of 2.5D surfaces,
i.e. surfaces that can be described by a 3D mathematical function of the
form z f(x, y). Regular raster grids describe a regularly sampled representation
of this function f which implicitly assumes a definition of a
projection (where the form z f(x, y) is valid) defining the expression of
the (x, y) coordinates from the initial 3D coordinates in a global Cartesian
reference system. When the surface describes the Earth’s relief this projection
is a map projection given an ellipsoid.
Indeed, RGs have the geometry of an image where the pixels are the
nodes of the regular raster grid and the grey values of the pixels represent
the elevations. Indeed, one of their main advantages is that they can
be visualized as grey-level images or in colour with a look-up table, e.g.
hypsometric. They should also preferably, for data size reasons, be stored
as images. To pass from the image to the grid geometry and information,
some parameters (x0 , y0 , dx, dy, b) and the units in which these parameters
are expressed, in addition to the map projection system and to the
ellipsoid parameters, have to be known and stored either in the image/grid
header or aside in a separate file. The transformation from the image coordinates
of pixel (i, j) to corresponding 3D coordinates (x, y, z) can be
expressed as:
x i dx x 0
y j dy y 0
Overview of digital surface models 161
z G(i, j) dz b. (3.1)
G(i, j) is the grey level of pixel (i, j). (x 0 , y 0 ) are the spatial coordinates of
the image’s first row and line pixel. (dx, dy, dz) are the spatial sampling
of the grid respectively along the x, y and z axes. b is the elevation corresponding
to the grey-level 0 in the image. The dz and the b parameters
are necessary if the grey levels are not coded as floating values but as 8
or 16 bits integers.
As all sampled models, a raster grid can describe many possible surfaces.
This problem arises when we want to determine the elevation of a point
falling inside the grid in between the known nodes of the grid. The elevation
has to be calculated from the elevations of the neighbouring grid
points with an interpolation function (bilinear, bicubic, etc.).
The problem with the RG models is that the spatial sampling of the
grid is regular and thus some features of the landscape can be correctly
described at a given spatial sampling while some others, smaller, would
not be relevantly sampled thus smoothed or even missing in the sampled
model. Using the same density of samples all across a changing landscape

162 Nicolas Paparoditis and Laurent Polidori
is definitely a limit of these models. Adaptive sampling meshes are more
adapted to describe an irregular world. The distribution of elevation points
needs to be dense on rough relief areas and only sparse on smooth areas.
Indeed, the points do not need to be dense but to be well chosen to describe
the surface as well as the application requires.
Moreover, an underlying hypothesis made in aerial photogrammetry is
that we suppose that the surface we are trying to model can be described
by a graph of the form (x, y, f(x, y)). Indeed, this hypothesis is not always
valid, e.g. in urban areas due to 3D discontinuities. It is even less valid in
the case of terrestrial photogrammetry where overlapping surfaces often
occur. RGs are an easy but not a general way to model surfaces.
3.1.3.2 Triangular irregular networks (TIN)
Most of the conventional data acquisition systems provide sparse point
measurements. Building a regular grid DSM from these samples is thus often
against nature. The idea of triangular irregular networks is to adapt completely
the model to the samples by describing the surface by elementary
triangles where the vertices are the samples themselves. These triangles can
be constructed from the samples limited to their planimetric components
by a 2D Delaunay triangulation process (a very good triangulation algorithm
is available on the web site of the Carnegie Mellon University) if the surface
is 2.5D and by a more complex 3D Delaunay triangulation process, also
called tetraedrization, if not. This triangular modelling is widespread and
extremely popular in virtual reality and in CAD world and systems.
The triangles built by a triangulation process have only the aim of defining
neighbourhoods in which one can directly calculate the elevation using
an interpolation function between the three vertices for a given (X, Y).
The simplest interpolation function is the following. Let T(P1 , P2 , P3 ) be
the considered triangle where P1 (X1 , Y1, Z1 ), P2 (X2 , Y2, Z2 ), P3 (X3 , Y3, Z3 )
are the three triangle vertices. Let V((X1 ,Y1 ,Z1 ) (X,Y,Z)), V1 {(X2 Y2 ,
Z2 ) (X1 , Y1 , Z1 )), V2 ((X3 , Y3 , Z3 ) (X1 , Y1 , Z1 )), and (, , ) be the
barycentric coordinates of point P inside T. V lies inside the plane defined
by (V1 , V2 ) if V can be expressed in a unique way under the form V
V1 V2 where:
(V1∧V2 )k and v (V∧V1)k (V2∧V1 )k where k 0
0
1 .
(V∧V 2)k
(3.2)
Thus Z (V 1 V 2 )k.
Contrary to RGs, the samples and the set of triangles could be nonordered,
thus leading to more time-consuming elementary operations as
interpolating the Z elevation value for a given (X, Y). Indeed all triangles
have to be parsed to determine the whole set of triangles including this

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point. For a given (X, Y) and for each triangle T within the set of triangles
we can calculate the coordinates of P(X, Y, Z) belonging to the plane lying
on T as described above. Under the assumption that the surface is 2.5D,
the parsing of the set of triangles can be stopped when P(X, Y, Z) belongs
to T which is verified if and only if:
1 0
0
0 .
Overview of digital surface models 163
(3.3)
Adding some easy topology (ordering information) by storing for each
triangle the index of the three adjacent triangles limits considerably the
number of triangles to be parsed. Indeed, let us consider a triangle T 0 . We
would like to determine the triangle T containing the point (X, Y). Starting
from T 0, we will look for the adjacent triangle T 1 of T 0 in the direction
of (X, Y). We will start this process again from T 1 and again until the
current triangle contains (X, Y). This is also a way of parsing the triangles
to generate an elevation profile between two 3D points on the surface.
Some further topology that we will call spatial indexing can accelerate
in an impressive way the number of triangles to test. Indeed, the 2D
(x, y) space can be regularly and recursively split, e.g. in a dichotomy
process, in square bounding boxes and the patches can be sorted in a tree
graph where every branching node would represent a rectangular bounding
box – which would get smaller while climbing up in the tree – and where
the leaves at the end of the branches would be the patches themselves.
One should remark that a patch/leaf could belong to several boxes/
branches. We here obtain a hybrid mix of an irregular sampling with a
regular ordering which keeps at the same time the useful flexibility of
adaptive meshes to describe the relief variations, and the rapidity to access
to interpolated information.
This spatial indexing can also be given by an index raster map giving
for each (X, Y) node of the map grid the index of the corresponding
triangle. This map can be constructed by filling each triangle (limited to
its planimetric components) with the label/index value of the triangle inside
the map grid. The quality of this map will depend on its spatial sampling
considering the aliasing problems arising close to the triangle limits.
A drawback of raw TIN models is that the slope is identical on the
whole facet surface and the slope is discontinuous between adjacent facets.
If we suppose that our sample acquisition technique provides us in addition
the surface normal vector and if we assume that the surface is smooth
and curved inside the facet and/or across the facets, we can improve the
surface approximation by adding to each triangle some more parameters
to model locally the behaviour of the surface by an analytical function,
e.g. bicubic splines, compatible in continuity and in derivability to all adjacent
facets.

164 Nicolas Paparoditis and Laurent Polidori
3.1.3.3 Surface characteristic lines
A surface can also be described by characteristic feature lines (or points)
and by contour lines (also called soft lines) giving the intersection between
the surface and planes regularly sampled in one direction. This modelling
is valid if the surface is 2.5D. Contour lines can be directly acquired from
manual stereo-plotting of a stereopair, through analogue, analytic, or digital
devices, derived from a regular grid or a TIN model DSM, or digitized
manually or automatically from scanned maps. The reconstruction of a
surface from contour lines is well conditioned if the surface is smooth. If
not the addition of characteristic breaking lines (also called hard lines),
e.g. slope break lines, helps in the regularization of the reconstruction
problem by describing the surface local high derivatives.
Modelling a surface in this way can also be seen as a data compression
of the true surface. And the density of contour lines can be seen as a data
compression rate vs. a data loss ratio.
To conclude, the choice of one of these models and on its parameters
will depend on the 3D geometric particularities of the object to model, on
the requirements of the application using the model, and will have a definite
impact on the surface approximation accuracy and on the data storage
size.
3.2 DSM QUALITY: INTERNAL AND EXTERNAL
VALIDATION
Laurent Polidori
3.2.1 Basic comments on DSM quality
Many different techniques can be used to extract a DSM, depending on
available data, tools or know-how: map digitization and interpolation,
optical image stereo correlation, shape from shading, interferometry, laser
altimetry, ground survey, etc.
In spite of their variety, each of these techniques can be described as a
two-step process:
• the first step consists in computing 3D locations for a large number
of terrain points;
• the second step consists in resampling the resulting data in order to
fit a particular grid structure and a particular data format.
Therefore, the quality of a DSM is the result of the way these two steps
have been carried out.

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What is the quality of a digital surface model? Basically, it is its capability
to describe the real surface, but quality criteria cannot be defined
without keeping in mind user requirements. The impact of DSM quality
on the reliability of derived information (such as geomorphology or hydrography)
has been analysed by many authors to improve the understanding
of what DSM quality means (e.g. Fisher, 1991; Lee et al., 1992; Polidori
and Chorowicz, 1993).
The relevance of a criterion depends on the way it reflects these requirements,
and on the feasibility of an efficient validation to check its fulfilment.
3.2.2 Quality factors for DSM
DSM quality 165
As recalled above, the quality of a digital surface model is affected by both
point location accuracy and resampling efficiency.
Point location accuracy
Each point location technique has a specific error budget, with contributions
from the intrinsic features of the employed system (sensor, platform,
etc.) and from the acquisition and processing parameters.
Most DSM extraction techniques (and particularly photogrammetric and
profiling techniques) are direct techniques, which means that they provide
point location measurements in which adjacent samples are independent
from each other. They are more suitable for elevation mapping than for
slope mapping. On the contrary, differential techniques (such as shape
from shading or radar interferometry) provide information about surface
orientation, i.e. slope or azimuth. In this case, elevations are obtained by
slope integration, so that height errors are subject to propagation. This
phenomenon may be reduced by crossing different integration paths.
As far as resampling is concerned, its impact on DSM quality depends
on grid geometry (structure and density) and on data format.
Grid structure
A great variety of grid structures has been proposed for digital surface
model resampling. They have been reviewed and discussed by several
authors (Burrough, 1986; Carter, 1988). Three main approaches can be
mentioned:
• regular sampling, in which all meshes have constant size and shape
(most often square);
• semi-regular sampling, which is based on a very dense regular grid in
which only useful points have been selected;
• irregular sampling, where terrain points may be located anywhere.

166 Laurent Polidori
Regular sampling has obvious advantages in terms of storage, but it is not
very efficient to depict natural relief in which shapes and textures are mainly
irregular, unless the grid is considerably densified. This is the reason why
semi-regular methods like progressive or composite sampling (Burrough,
1986; Charif and Makarovic, 1989), and irregular ones like TINs
(Burrough, 1986; Chen and Guevara, 1987) are so successful for digital
terrain modelling.
Grid density
The density of a DSM is basically a trade-off between economical
constraints (which in general tend to limit the density) and accuracy requirements
(which are rather fulfilled by a higher grid density).
The impact of mesh size on DSM quality has mainly been studied in
terms of height error (e.g. by Li, 1992), but its major effect is on height
derivatives. Indeed, reducing the density of a DSM grid (i.e. subsampling)
removes the steepest slopes and makes the surface model smoother.
Data format
The digital format of the data has to be mentioned as well within the
contributors to DSM quality, and in particular the number of bytes per
sample. Formats using 2 bytes (i.e. 65,536 levels) which allow a 10 cm
precision over an elevation range of more than 6,000 m, are commonly
used because they provide a good trade-off between 1 byte (which limits
the accuracy) and 4 bytes (which increases the volume of data needlessly).
3.2.3 Internal validation
A set of 3D coordinates drawn at random has very little chance of yielding
a realistic relief. Therefore, it is worth checking that the terrain described
by the DSM is possible, i.e. that it fulfils the main properties of real topographic
surfaces. These properties can be quite straightforward. For
instance ‘rivers go down’ or, in urban areas, ‘building walls are vertical’.
Checking to what extent these properties are respected does not require
reference data but only a generic knowledge of landscape features. For
this reason, it can be called internal validation.
Visual artefact detection, which should always be done before DSM
delivery, is the first level of internal validation.
Unrealistic textures, such as strips or other anisotropic features, can be
revealed by Fourier analysis or by comparing variograms in different directions.
These artefacts can result from image scanning (Brown and Bara,
1994) or from contour line interpolation (Polidori et al., 1991).
If some rules are universal (e.g. rivers go down), others require an expert
knowledge about geomorphology (for natural relief mapping) or about

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urban structure design (for building extraction). For instance, texture
isotropy is not supposed to be fulfilled everywhere, so that some subjectivity
is required to distinguish natural anisotropies from directional
artefacts. This distinction will be easier if the DSM extraction algorithms
are known, because each extraction step may have a contribution to the
observed artefacts: correlation noise, original image striping, grid resampling,
etc.
3.2.4 External validation
If external elevation data are available and reliable, an external validation
can be considered, which consists in comparing the DSM with the reference
data. This is the most usual way of evaluating the quality of DSMs,
but it is limited by two major difficulties.
The first difficulty is the availability of a suitable reference data set.
Indeed, DSMs are often validated with very few ground control points, so
that the comparison may be statistically meaningless. Moreover, these
control points have their own error which in most cases is not known and
which may have the same order of magnitude as the DSM they are supposed
to control.
The second difficulty is the need for an explicit comparison criterion,
which must reflect application requirements. On the one hand, the magnitude
to be compared has to be defined: it is altitude in most cases, but
slope or other derivative magnitudes could also be considered. On the
other hand, a statistical index has to be defined too, generally based on
the histogram of height differences: mean, standard deviation, maximum
error, etc. have different meanings.
An interesting way of overcoming these difficulties is to map the discrepancies
in order to display their spatial behaviour. This validation approach
is not quantitative, but it proceeds very useful information, such as which
landscapes (in terms of relief shape but also land cover) are accurately
depicted and which are poorly shown. Therefore, it may contribute to
improve the understanding of a given DSM extraction technique.
References
DSM quality 167
Brown D., Bara T. (1994) Recognition and reduction of systematic error in elevation
and derivative surfaces from 7 1/2 minute DEMs. Photogrammetric
Engineering and Remote Sensing, vol. 60, no. 2, pp. 189–194.
Burrough P. (1986) Principal of geographic information systems for land resources
assessment. Oxford University Press, New York.
Carter J. (1988) Digital representations of topographic surfaces. Photogrammetric
Engineering and Remote Sensing, vol. 54, no. 11, pp. 1577–1580.
Charif M., Makarovic B. (1989) Optimizing progressive and composite sampling
for DTMs. ITC Journal, vol. 2, pp. 104–111.

168 Laurent Polidori
Chen C., Guevara J.A. (1987) Systematic selection of very important points (VIP)
from digital elevation model for constructing triangular irregular networks.
Proceedings of Auto Carto 8, Baltimore, 29 March–3 April, pp. 50–56.
Fisher P. (1991) First experiments in viewshed uncertainty: the accuracy of the
viewshed area. Photogrammetric Engineering and Remote Sensing, vol. 57, no.
10, pp. 1321–1327.
Lee J., Snider P., Fisher P. (1992) Modelling the effect of data error on feature
extraction from digital elevation models. Photogrammetric Engineering and
Remote Sensing, vol. 58, no. 10, pp. 1461–1467.
Li Z. (1992) Variation of the accuracy of digital terrain models with sampling
interval. Photogrammetric Record, vol. 14(79), pp. 113–128.
Polidori L., Chorowicz J., Guillande R. (1991) Description of terrain as a fractal
surface and application to digital elevation model quality assessment. Photogrammetric
Engineering and Remote Sensing, vol. 57, no. 10, pp. 1329–1332.
Polidori L., Chorowicz J. (1993) Comparison of bilinear and Brownian interpolation
for digital elevation models. ISPRS Journal of Photogrammetry and
Remote Sensing, vol. 48(2), pp. 18–23.
3.3 3D DATA ACQUISITION FROM VISIBLE IMAGES
Nicolas Paparoditis, Olivier Dissard
Introduction
The surface that can be processed from images is an observable surface.
In the case of aerial visible images, this surface will describe the terrain
but also all the structures lying on the terrain at the scale/resolution of
the images e.g. buildings, vegetation canopy, bridges, etc.
The techniques presented here are applicable to visible images of all
platforms (helicopters, airplanes, satellites, ground vehicle, ground static,
etc.) and of all kinds of passive sensors (photos, CCD pushbroom, CCD
frame cameras) as long as the internal, relative and external parameters
for each view are known. In other words, we suppose that the platformtriangulation
process has already been achieved previously. Nevertheless,
even though the concepts remain the same, the 3D processes and the integration
of the processes themselves can change slightly, depending on the
survey acquisition possibilities and constraints. We will point out whenever
the particularities of the sensor and the platform have an impact on
the processes described.
Besides the particular process assessment induced by the particular geometry
and distribution of the data, the methods and the strategies to be
involved also depend on what kind of 3D data we want to derive from
the visible images, i.e. single-point measurements or more dense and more
regular for the generation of a DEM. We will start from the simplest, the
stereopair processing of an individual 3D measurement, before looking at

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the global processing for the generation of an elementary stereopair DEM
and a global DEM over the survey, and we will end by defining the proper
specifications for a survey acquisition system (and the processes to manage
them) enabling the processes to avoid in a clean way all (or at least most)
of the problems and allowing us to reach the automation of a complete
and robust enough DEM on the whole survey.
3.3.1 Formulation of an automatic individual point
matching process
Nicolas Paparoditis
The major interest of digital photogrammetry, besides all the management
facilities that it provides, is that images are described by a set of regularly
spaced digital values that can be easily manipulated with algorithms. Let
I 1 and I 2 be the two digital images composing the stereopair, (i, j) a point
position in one of the image grids, and R(i, j) the corresponding grey-level
value.
The concern of digital matching, is how do we determine that any point
(i 1, j 1) of I 1 and point (i 2, j 2) of I 2 are alike or homologous? And more generally,
how do we determine that characteristic features of I 1 and I 2 are alike? This
preoccupation is one of the most recurrent in digital photogrammetry, image
processing and in automatic pattern recognition techniques.
Entity attributes and similarity measure
As we are looking for individual point matches, we will stick for now with
point entities. Most of the time a function f derives from image measurements
(values) on or around our point entities (i1, j1) and (i2, j2) corresponding
entity attribute vectors V1 and V2 . Then a similarity function g
(g can be a distance but does not have to be) derives a numerical similarity
value (or score) C describing the similarity between V1 and V2 and
thus the entities themselves. C can be expressed as follows:
C((i 1, j 1), (i 2, j 2)) g(V 1, V 2).
3D data acquisition from visible images 169
Interpolation function
We point out that the image sampling effects are such that the real homologue
(i2, j2) of a point (i1, j1) on the grid of image 1 is not itself on the
grid in image 2. Thus the function f should implicitly use and be built on
an interpolation function V (bilinear, bicubic, sinc, etc.) which determines
the intensity value in any sub-pixel point of an image from its closest
neighbours on the image grid.

170 Nicolas Paparoditis and Olivier Dissard
An ill-posed and a combinatorial problem
In practice, how do we build V and choose f ? Let us take as an example
the simplest f and g. For instance, f giving the intensity value itself and g
the difference between the intensity values. Due to the image noise, the
radiometric quantification, and the image sampling, the grey-level values
themselves for real homologous points are in general different. Thus, many
points in I1 will have close intensity values and for a given point in I1 many points in I2 will have close intensity values. Thus we have a serious
matching ambiguity problem and we can conclude that the information
derived from f is not characteristic enough and g not stable and discriminating
enough. We also face a combinatorial explosion especially if we
want to match all points of I1. The problem of digital image matching belongs to the family of mathematically
ill-posed problems (Bertero et al., 1988). The existence, the
uniqueness, the stability of a solution are not a priori guaranteed. This
problem can be transformed in a well-posed one by imposing regularizing
constraints to diminish the degrees of freedom in the parameter space so
that the domain of possible solutions can be reduced (Tikhonov, 1963).
Area-based matching: a first solution to ambiguity
One solution to this matching ambiguity problem is to make the entities
attribute vectors as unique as possible. Instead of matching the grey level
of the pixel, we can match the context (all the grey levels) around the
homologous points. We here make the assumption that the contexts are
also homologous. The context is most of the time characterized by all the
grey levels of the pixels inside a rectangular (most of the time square)
template window (also called image patch) centred on the entity thus with
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v(i, j) = 60
⎟
⎜ ⎟
⎜76
⎟
⎜ ⎟
⎜51
⎟
⎜54
⎟
⎜ ⎟
⎝56
⎠

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an odd number of lines N and rows M. The entity can be described by
a vector v with N × M components. Each component is a grey level of a
template pixel following a given spatial ordering (as shown in Figure 3.3.1).
Thus, the vector describes the local image texture pattern, which is of
course much more discriminating than a single intensity value. The larger
the templates, the higher the discrimination power. Meanwhile, our context
stability assumption becomes less and less valid (see ‘Geometric assumptions’
hereunder).
Matching the entities is equivalent to matching their area context vectors.
Matching these vectors is what we call area-based matching. The requirement
for area similarity functions is that their response is optimal for real
homologous points and that they are as stable as possible to some radiometric
and geometric changes between homologous template areas in both
images. The most commonly used similarity functions on these areas are
the following:
Least squares differences:
C1((i1, j1), (i2, j2))
Scalar product:
|| ; (3.4)
V2(i2, j2) V2(i2, j2) V 2
1(i1, j1) V1(i1, j1) ||
||
3D data acquisition from visible images 171
C2((i1, j1), (i2, j2)) . (3.5)
V 2
1(i1, j1)V2(i2, j2) V 1 (i 1 , j 1 ) V 2 (i 2 , j 2 ) ||
As shown in Figure 3.3.2, these similarity functions have a geometrical
explanation. C 1 is the norm of V 3 and C 2 is cos , where is the angle
between V 1 and V 2. When the textures are alike V 1 and V 2 should be
nearly collinear. Thus C 1 should be close to 0 and C 2 close to 1.
If corresponding templates have the same texture but are affected by a
radiometric shift (case where V 1 ~ V 2 ), due to the fact that the images
could be acquired with different lighting conditions or in the case of
0
v 1
Figure 3.3.2
θ
v 3
v 2

172 Nicolas Paparoditis and Olivier Dissard
analogue photographs that the images have been scanned in different conditions
or that the observed surface has a non-Lambertian behaviour, the
similarity scores will decrease significantly thus altering the discrimination
process. To overcome this problem the vectors can be centred. Thus if 1
(resp. 2 ) is the mean grey level and 1 (resp. 2 ) is the root mean square
of grey levels of the template around (i 1 , j 1 ) (resp. (i 2 , j 2 )) the previous similarity
functions become:
Centred least squares:
C′ 1((i1, j1), (i2, j2)) || ; (3.6)
V2(i2, j2) 1 V 2
1(i1, j1) 2 ||
Linear cross-correlation:
V
C′ 2((i1, j1), (i2, j2))
1(i1, j1)V2(i2, j2) 12 . (3.7)
Could not the images be pre-processed with a global histogram radiometric
equalization instead of centring each vector? Indeed not! This
process would alter the image quality and consequently the quality of the
matching process. Furthermore, some of these effects change through the
images, i.e. hot spot and non-Lambertian effects. Could the contrasts be
enhanced? No! In general we do so when we look at an image, because
of our non-linear and low differential eye sensibility. Nevertheless, a correlation
process has no such problems.
Image matching definition
Under the assumption the matching problem is well posed, if (i2, j2) is the
homologue of (i1, j1) inside the admissible domain of hypotheses S within
I2 then one of the two following expressions should be verified for a given
similarity function C:
or
(i 2, j 2)
ArgMax
(i, j)∈I 2 /S
(i2, j2) ArgMin C V1(i1, j1), V2(i, j) . (3.8)
(i, j)∈I 2 /S
1
1 2
C V 1(i 1, j 1), V 2(i, j)
Geometric assumptions
The area-based matching process described above rests upon a major
assumption. Indeed, we have implicitly supposed that the homologous
2

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3D data acquisition from visible images 173
template of image 1 can be found in image 2 by a simple shift. In general,
the differences in the viewing geometry (due to erratic variations of attitude
of the sensor) between the two views and the deformations due to the
landscape relief are such that this assumption is not strictly verified.
Feature-based matching
If the point entity itself is or belongs to a characteristic image feature, e.g.
an interest point (see §2.4) or a contour point, the homologous point can
be looked for in the set of identical image feature entities in the other
image. This will restrict the combinatorial problem and thus the ambiguity
problem. Furthermore, these entities are less sensitive to geometric
deformations between the images. Information such as local gradient norm
or direction, second or higher degree image derivatives can be used to
build the feature entity attribute vectors. Nevertheless, in an urban landscape
for instance, many image features look alike and finding characteristic
and discriminating entity attributes is difficult and sometimes impossible.
Moreover, the entities themselves, e.g. building contours, are not stable
thus the ambiguity problem remains. Feature-based matching is also an
ill-posed problem and is limited to a sparse set of points in the scene and
thus does not provide the universality of area-based techniques for matching
every point in the scene or in the images.
Stereopair geometric constraints: a second solution to the
ambiguity problem
Another way of limiting the ambiguity problem is by reducing the combinatory
of the matching problem, i.e. the search space for homologous
points. Indeed, the bigger the search space the higher the number of possible
homologous hypotheses and the higher the probability of encountering
matching ambiguities.
The following paragraphs describes the different matching methods that
can be applied to an oriented stereopair to overcome the geometric distortion
problems and to restrict the spatial domain S of homologous solutions.
Generally the point-to-point matching problem in a stereopair geometry
can be expressed in two radically different ways and thus leads to two
different matching methods each having different advantages.
3.3.2 Stereo matching from image space (SMI)
Nicolas Paparoditis
This first method only requires the relative orientation of the images for
the matching process. If the real 3D localization is meant to be computed,
the absolute orientation of the images are required. The matching

174 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.3
P 1 (i 1, j 1)
C 1
O 1
formulation of this method, which is image-based, can be expressed in the
following terms: ‘given a (i 1, j 1) in I 1 (called the master or reference image)
what is the corresponding (i 2, j 2) in I 2 (called the slave or secondary image)?’
Epipolar lines
The position of (i2 , j2 ) is geometrically (stereoscopically) constrained by
(i1, j1). As we can see in Figure 3.3.3, all possible matches are on a line
denoted E in the image 2, called the epipolar line, which is the projection
in the image plane of the 3D plane lying on the 3D ray of (i1 , j1 ) including
C1 and on C2 . Due to geometrical distortions of the optics, this line is
more likely to be a curve. Nevertheless, the general 2D matching problem
is now transformed into an easier 1D matching problem where (i2 , j2 ) has
Figure 3.3.4
C 1
C 2
E
O 2
C 2
Motion

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Figure 3.3.5
O′ 1
C 1
P 1(i, j)
O 1
y
3D data acquisition from visible images 175
P′ 1(i′, j′)
z
to be searched for along this curve. Note that all epipolar lines corresponding
to all points of image 1 intersect themselves in a point of image
2, called epipolar point, which is the projection of C 1 in the image 2 plane
(see Figure 3.3.4).
If I 1 and I 2 are two consecutive images in the same aerial flight strip
(near to vertical viewing axis), or classical across track (up to 50° of latitude
so that we can consider the orbits to be locally parallel), or along
track satellite stereopairs, homologous texture vectors of a given landscape
patch (with a low slope) can be found by a simple translation. Thus our
previous correlation scores similarity criteria can be applied directly. In
these cases, the epipolar lines are very close to the image lines themselves.
Nevertheless, for some aerial surveys, the differential yaw – but also
pitch and roll – angles between both views, due to plane instability, can
sometimes occur. The higher the difference is and the larger the window
size gets, the less the texture vectors for homologous points will look alike,
and the more the automatic matching process is unlikely to give good
results. In these conditions to overcome this problem, a gyro-stabilized
platform can be used so that epipolar lines follow as closely as possible
the image lines (see Figure 3.3.5).
Epipolar resampling
To ease the algorithmic implementation of the matching process, the images
are often resampled in a way that the epipolar lines become parallel and
aligned on the image lines. Let I′ 1 and I′ 2 be the resampled images. Thus
looking for the homologous estimate of point (i1, j1) can now be expressed:
x
O′ 2
C 2
O 2

(î 2, j , (3.9)
where N is the number of rows of I′ 2 .
How can we manage this resampling? Let (O1 , i1 , j1 , k1 ) and (O2 , i2 , j2 ,
k2) be the two reference systems describing the orientation of the image
planes. We simulate for each view the image of a virtual sensor (I′ 1 and
I′ 2) with the same optical centres but with new reference systems and
without distortions of the optics and of the focal plane. The new reference
systems (O1, i′ 1, j′ 1, k′ 1) and (O2, i′ 2, j′ 2, k′ 2) are constructed so that i′ 1
and i′ 2 are collinear to C1C2 , k′ 1 and k′ 2 are collinear to z, and j′ 1 k′ 1 ∧
i′ 1 and j′ 2 k′ 2 ∧ i′ 2 .
How do we construct the pixel grey levels of these new images? For
each pixel P′(i′, j′) of image I′, we determine with our new sensor’s geometry
the corresponding ray in 3D taking into account the distortion of
the camera. According to previous geometry, we determine the corresponding
image position P(i, j) in image I by intersecting the 3D ray with
its image plane. Of course, this point falls anywhere inside the image grid,
thus the grey-level value for P′(i′, j′) has to be calculated by interpolation
of the grey-level values of neighbour nodes of P(i, j) inside the image grid.
If it can be avoided, in the case of classical good conditions surveys, it
is preferable. Indeed, this operation leads to a degradation of image quality
which will alter slightly the quality of the image matching process. The
only advantage of a systematic epipolar resampling is that the images can
be viewed directly in digital photogrammetric workstations whatever the
differential yaw between the images. (See Figure 3.3.6.)
ˆ 176 Nicolas Paparoditis and Olivier Dissard
2) (î 2, j1) ArgOpt C V (i I′1 1, j1), V (x, j I′2 1)
x∈[0, N]
(a) (b)
Figure 3.3.6 Epipolar matching. The left image (a) and the right image
(b) extracts are the result of the stereopair resampling. The broken lines
correspond to the horizontal conjuguate epipolar lines in these resampled
images.

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P 1 (i 1, j 1)
C 1
O 1
Figure 3.3.7 Defining a search space interval.
3D data acquisition from visible images 177
O2 E′ (imin, (i j
min 1) ,j1) (imax, j1) Defining an interval for the match search
The range of positions for all possible homologous hypotheses for a given
P1(i1, j1) in I1 can be delimited inside an interval ([i2min, i2max], j1) on the
epipolar E′ by the knowledge of minimal and maximal z values (or the range
of disparities/parallax if we only have the relative orientations) on the scene
(as shown on Figure 3.3.7) if we want to have a given disparity range for
all the points in image I1, or a gross relief model if we want to have this
information more locally. This information could be provided by existing
databases, e.g. world-covering low-resolution DTM or by a map.
Another way of doing this, is to stereoplot manually the homologous
image points for the two landscape points corresponding to the lowest and
the highest point in the scene or plotting a larger set of points regularly
sampling the scene if we want to have a locally adaptive range definition.
Some more elaborate ways of reducing these intervals will be given in
§3.3.8.
Search-space sampling and homologous position estimation
If di is the spatial sampling in I2 along the search space interval [i2min ,
i2max], all the correlation scores for all the possible moves form a graph
usually called a correlation profile. The homologous point is considered
to be the point where the maximum of the similarity score (also called the
correlation peak) occurs (see Figure 3.3.8). Its position can be expressed
as follows:
C 2
Z min
Z max

178 Nicolas Paparoditis and Olivier Dissard
C
i min
d i
î 2
î 2subpix
î 2 ArgMax C2V′ 1(i1, j1), V′ 2(imink·di, j1)imin) . (3.10)
k∈[0,(imaximin)/di] The smaller the di the better the correlation profile is sampled and the
higher the matching precision. In practice, to limit the number of similarity
scores calculation, most of the time di is fixed to 1 so that all the
homologous points hypotheses fall on the grid and thus the texture vectors
are directly extractable from the images without any further interpolation
processing. If we consider the peak to be the integer position of the homologous
point, the maximum error in the homologous estimation is 0.5 pixels.
A more precise (in most cases) sub-pixel position can be found by fitting
a polynomial function, often a parabola, through the correlation values
around the peak position. The most commonly used fitting function is the
parabola. With the parabola, the sub-pixel position of the correlation peak
can be obtained from the discrete positions as follows:
C(î
î2Subpix î2
21, j1) C(î21, j1) . (3.11)
2C(î21, j1 ) C(î21, j1 ) 2C(î2 , j1 )
If the di sampling is sub-pixel, with the idea of finding directly a correlation
peak closer to the real homologous position without any a posteriori
interpolation, then the homologous hypotheses samples fall inside the grid
and thus all the components of the texture vectors have to be interpolated.
Generally a di of one-fifth of a pixel reaches the limit of the matching
process precision. One should remark that the grey levels of texture vectors
of image I2 will have gone through two interpolation processes. We have
pointed out earlier that a resampling alters the image quality and consequently
the matching quality. In this particular case, this direct sub-pixel
matching process should be carried out on the non-resampled images along
the epipolar curve E.
i max
Figure 3.3.8 Sub-pixel localization of the correlation peak.

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3D data acquisition from visible images 179
Doing the interpolation on the images or on the correlation profile,
provides very close results. If the matching process has to be carried out
on many points of image I 1 , one would prefer using the first technique as
the number of samples to be calculated is smaller.
Managing with relative orientation errors
Due to the relative orientation errors, the real homologue of (i1, j1) is not
on the computed epipolar line E′ itself but in a close range of the epipolar
line. To cope with that the search space can be extended to all points of
image I2 in a neighbourhood (depending on relative orientation residues;
1 pixel is usually enough) on each side of the epipolar line. Thus our correlation
profile becomes a correlation surface. If the peak of the correlation
surface occurs for a point on the epipolar line, the easiest way of finding
the sub-pixel position is to first determine the sub-pixel position in the
epipolar direction by fitting a parabola through the correlation scores and
then finding the sub-pixel position in the orthogonal direction by fitting
another parabola. If not the neighbourhood should first be extended before
a further process.
3D localization of homologous points
The 3D localization of homologous points (i1, j1) and (i2, j2) is obtained
by intersecting both corresponding 3D rays D1(C1, R1) and D2(C2, R2). If
(i2, j2) does not lie exactly on the epipolar line of (i1, j1), those rays do not
intersect, as shown on Figure 3.3.9.
P 1 (i 1, j 1)
C 1
O 1
R 1 D1
M 1
P(x, y, z)
D 2
M2 Relative error
Figure 3.3.9 3D triangulation and localization of homologous points.
R 2
O 2
C 2
P 2 (i 2, j 2)

180 Nicolas Paparoditis and Olivier Dissard
Let M 1 be the closest point of ray D 1 to ray D 2 and M 2 the closest point
of ray D 2 to ray D 1. M 1 and M 2 are such that:
⎧
⎪
⎨
⎪
⎩
M 1 C 1 1 R 1
M 2 C 2 2 R 2
M 1M 2 · R 1 0
M 1M 2 · R 2 0
⎧
⎪
thus ⎨
(3.12)
⎪
⎩ 2 (C1C2, R1, R1∧R2) (R1∧R2) 2 (R1∧R2) .
2
The corresponding 3D point is generally chosen to be P (M 1 M 2 )/2,
the closest and equidistant point to both rays. The ||M 1M 2|| distance gives
us a quality estimator of the 3D relative localization.
Relation between 3D precision and matching precision
The 3D localization precision is affected by the aerial triangulation errors,
the matching errors and its planimetric and altimetric components depend
on the viewing angles and on the stereoscopic base to height ratio (B/H)
as shown on Figure 3.3.10. Putting aside the errors due to the aerial triangulation
process, thus making the assumption that the relative orientation
is perfect, we can estimate theoretically the intrinsic precision of the
matching process. Let ematch (resp. ealti) be the matching (resp. altimetric)
error and match (resp. alti ) the root mean square of the matching (resp.
altimetric) error expressed in pixels and r0 the ground pixel size in metres.
Thanks to the Thales theorem, the altimetric error is given by:
ealti H
B r0 ematch and H
alti
B r0match .
1 (C 1C 2, R 2, R 1∧R 2)
The planimetric error depends on the position of (i 1, j 1) in image I 1:
eplani tan (i) · ealti OP1 ,
where f is the focal length expressed in pixels.
The formulas that we have expressed here are not the models of the 3D
errors that we would have if we intended plotting a given ground feature
in image I1 and finding automatically the 3D corresponding point. Indeed
the matched point (i2, j2) will correspond to (i1, j1) and not to the feature
that was meant to be plotted in image I1. This plotting error will inevitably
lead to another source of error in the 3D localization. Only the plotting
errors along the epipolar lines will influence the altimetric precision. Let
the parallax be p = O2P2 O1P1 and its errors along the epipolar lines
dp dp.i ematch eplottingi then the errors are given by:
ealti f

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P 1(i 1, j 1)
C 1
Figure 3.3.10
i
O 1
f
3D data acquisition from visible images 181
e alti
ealti H
B r0 dp and H
alti
B r0 √ 2 match 2 plotting
O2 ematch P 2(i 2, j 2)
. (3.13)
The higher the base to height ratio, the better the altimetric precision.
The choice of this ratio for a survey is conditioned by the desired quality
for the mapping output. For a DEM production line, for instance, a higher
one should preferably be chosen. Against that, when the ratio increases,
the image differences and consequently the matching difficulty increases.
(See Figure 3.3.11.)
Intrinsic matching precision
What is the precision that we can achieve from digital automatic matching?
The limits of the matching precision are easy to estimate in the best case,
i.e. when the homologous pattern can be found by a simple translation
(horizontal images planes, flat landscape). To generate a virtual global
translation between I1 and I2 , we can simulate a horizontal image plane
stereopair with perfectly known orientation parameters on a perfectly flat
landscape where we can map any kind of image pattern, e.g. an aerial
orthophoto. Since we have simulated the images, we know exactly the
translation value between I1 and I2. If we apply our matching process to
estimate these translations on different stereopairs simulated for different
translation values (fractional part between 0 and 1), we find systematic
errors in the translation estimation depending on the real translation fractional
part as shown in Figure 3.3.12.
B
r 0.e match
e plani
E′
P
C 2
H

182 Nicolas Paparoditis and Olivier Dissard
e plotting
P 1
C 1
Figure 3.3.11
Theoretic matching error (pixels)
0.6
0.4
0.2
–0.4
–0.6
O 1
B
P
e alti
e plani
This bias is due to the interpolation process and to the interpolation
function. We still have a bias if we do not use a sub-pixel estimator.
Indeed, if we do so we still implicitly use an interpolation function which
is the nearest-neighbour interpolator.
With the sub-pixel estimation process, the maximum bias occurs for a
sub-pixel translation of 0.25 pixels. The amplitude of this bias depends
O 2
P 2
C 2
e match
0 0.2 0.4 0.6 0.8 1
–0.2
Parallax fractional part (pixels)
Figure 3.3.12 Intrinsic matching errors.
H
sub-pixel match
pixel match

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on the interpolation function. It can range from 0.15 to 0.25 pixels. This
does not mean that the function giving the best theoretical precision is the
best in practice. In general, the simpler the interpolation functions (using
the smaller neighbourhoods) the more robust they are for real image digital
matching. From now on, we will consider that the average matching precision
is of a quarter of a pixel.
In the case of digital manual stereo-plotting, the matching precision is
difficult to evaluate statistically because of all the factors to be taken into
account: the radiometric (contrast), geometric (punctual, linear, corner,
etc.) and 3D context characteristics of the feature to be plotted, the image
quality (noise, blur, etc.), the stereoscopic acuity and the tiredness of the
operator, the optical quality of the stereo display, the sub-pixel possibilities
of the stereo display (sub-pixel image displacement, etc.), and the
plotting methodology. But in fact, most of these difficulties are present
with automatic matching techniques too.
3.3.3 Stereo matching from object space (SMO)
Nicolas Paparoditis
Photogrammetrists may express the matching problem for the 3D localization
in a completely different way. In fact, the other way round: ‘given a
(X, Y) in object space what is the corresponding z?′. As we can see in Figure
3.3.13, for a given (X, Y) if we change the z value, the displacements of the
corresponding image points are implicitly constrained along the curves
which are the projection of the planes lying upon each nadir axis and
(X, Y, z). Looking for the best z, is thus looking for the best image match
along these ‘nadir’ curves. Thus as for the image matching process guided
from image space, we build a correlation profile but instead of computing
all correlation scores for all the possible parallaxes along the epipolar line
we compute all correlation scores for all possible z values in a [z min, z max]
search space interval. The best elevation estimate is given by:
where
and
Loc I1 : ℜ 3 → I 1 (x, y, z) → (i 1, j 1)
Loc I2 : ℜ 3 → I 2 (x, y, z) → (i 2 , j 2 )
3D data acquisition from visible images 183
zˆ(X, Y) ArgMax C2V2(Loc (X, Y, z)), V I2 1(Loc (X, Y, z)) ,
I1
z∈[zmin,zmax] (3.14)
are the object to image localization functions. One should remark that
with this stereo method guided from object space, the image matching and

184 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.13
x
z
y
O 1
C 1
the 3D localization processes are performed at the same time. The elementary
sampling dz along the vertical line can be determined to be:
dz , (3.15)
where r0 H/f is the ground pixel size.
H
4B r0 Resampling correlation templates
Due to the perspective deformations and to the relative rotation between
image planes, the image patches corresponding to a flat square ground
patch ds do not overlap. Thus to obtain the best and the most discriminating
correlation score between those patches, the images are locally
resampled.
Indeed, as shown in Figure 3.3.14, we build two ortho-templates centred
on (X, Y). The image resolution of these templates is equivalent to that of
the images. For each pixel of these two ortho-templates we determine the
3D position on the ground patch, and we assign to each of them the greylevel
value for the corresponding image position. If our local flat ground
assumption is correct these should geometrically be exactly overlapping.
Stereo matching from object space is the proper way of obtaining automatically
3D measurements in a stereo display. Indeed, the observation
dz
(X, Y)
O 2
C 2
Z max
Z min

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Figure 3.3.14
x
space in a stereo display is directly the object space. The operator can, in
real time, obtain the elevation corresponding to a given plotter position
(X, Y) or can plot a flat line and have the 3D profile along this line, e.g.
for volume calculations or for road elevation profile estimation.
3.3.4 Difficulties due to image differences
Nicolas Paparoditis
z
P 1 (i 1, j 1, g 1)
y
3D data acquisition from visible images 185
O 1
C 1
(X, Y)
ds(z)
Classical template matching suffers from a certain number of defaults, due
to the non-respect of the assumptions it relies upon, that is to say the
geometric and radiometric similarity of templates centred on homologous
points and the discrimination power of correlation scores computed on
the radiometric templates. Sometimes, the landscape properties and the
geometric configurations of the image views are such that these assumptions
are not respected, and thus the similarity, existence and uniqueness
constraints for homologous points solution are violated:
• On homogeneous areas and periodic structures. The template radiometric
content does not ensure a possible discrimination between all
possible matches that fall in this area. The uniqueness constraint is
violated. Having a higher image quality or a larger window definitely
reduces the ambiguities for homogeneous areas. Periodic structures
are a problem when the spatial periodicity orientation is along the
O 2
C 2
P 2 (i 2, j 2, g 2)
Ortho-template of image 1 1
Ortho-template of image 1 2

186 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.15 Homogeneous surfaces and repetitive structures.
baseline. Having another view not on the same stereo baseline will
considerably reduce the ambiguities. (See Figure 3.3.15.)
• On hidden areas. In urban areas, for instance, all points observable
in an image do not always exist in the other image. Especially in urban
areas some zones are not seen on both images. Template matching is
a low level process. Even if there are no possible matches for a given
(i 1 , j 1 ) or for a given (X, Y), we will still have a maximum peak in the
correlation profile or surface which will lead to a false match. The
existence constraint is violated. A way of bypassing this problem, is
to have a higher stereo overlap (or more generally along or/and across
track multi-stereo views) so that at least every point of the scene can
be seen in at least two images, or to use multi-stereoscopic techniques.
(See Figure 3.3.16.)
• On non-overlapping areas. The incomplete overlapping of the stereopair
is one of the problems that occurs in digital stereo matching.
Indeed, many points of both images having no homologous solutions
will lead to problematic mismatches. The existence constraint is
violated.
Figure 3.3.16 Mobile vehicles and hidden areas.

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3D data acquisition from visible images 187
Figure 3.3.17 Differences in size and in shape of two real homologous patterns
on steep sloped surfaces.
• On steep sloped surfaces. The image pattern shapes corresponding to
a sloped planar ground patch in object space are geometrically not
alike. These deformations are accentuated when the slope rises. Thus
square image templates centred on homologous points have less
probability of looking alike when their size increase. The similarity
constraint is violated. A solution is having higher quality images so
that we could take smaller windows, or coping with the deformations
by using adaptive shape windows. (See Figure 3.3.17.)
• Areas around 3D discontinuities. When a template overlaps a 3D elevation,
as all the pixels contribute to the matching process, the elevation
determined in these areas will be a ‘mean’ of all 3D elevations inside
the templates weighted by the contrast distribution. This will lead to
a smoothing of the 3D relief morphology or to a spatial shift of the
3D structure of one half of the window size, as shown in Figure 3.3.18.
We can overcome this problem using small window sizes thus assuming
again high image quality, or using adaptive shape windows.
• Non-Lambertian surfaces. This happens for areas that have anisotropic
surface reflection properties. If we observe this surface from different
viewpoints, the radiometric measurements can be radically different.
When the images are not saturated, and if the non-Lambertian effects
are due relatively to a smooth surface compared to the ground pixel
size, template matching can still be used if the texture vectors are
centred to correct the radiometric bias between both homologous
templates. When some areas are saturated (no details) in one of
the images or when the non-Lambertian effects are due to 3D microstructures,
for instance a cornfield seen under two different viewing
angles, there is no satisfactory way of finding a good solution other

188 Nicolas Paparoditis and Olivier Dissard
(i, j) (i′, j′)
(i′′, j′′)
Figure 3.3.18 Matching areas around 3D changes. If we are looking for the
homologous template of (i, j) along the epipolar line, the best
correlation score will be obtained for (i′′, j′′) instead of (i′, j′). Thus
the parallax/elevation associated to (i, j) will be the one of the
rooftop.
than rejecting the matches for these areas, unless we consider another
stereopair if we have a survey with a high stereo overlap, or if we are
in any multi-stereoscopic configuration.
• Moving vehicles and shadows. Matching problems can occur due to
the fact that stereopairs are not instantaneous. Indeed, features like
vehicles and shadows can move from one image to the other. Some
vehicles appear or disappear, thus the existence constraint is violated.
For some vehicles moving along the baseline, the matching process
will generate aberrant corresponding 3D structures integrating the 3D
and the movement parallax. For satellite or aerial across track stereopairs,
shadows have moved thus the matching process can reconstruct
3D shadow limits at non-realistic elevations.
3.3.5 Coping with the problems: analysis of the correlation
profile
Nicolas Paparoditis
One of the easiest solutions to coping with these problems is to be able
to detect and reject all the matches where we think that the probability
of encountering a problem is high. We can study the morphologic structure
of the correlation profile and verify that it respects the properties of
a good match, i.e. high score for the maximum peak, large correlation
principal peak, no high secondary peaks. Many correlation profiles whatever
the area do not respect this model. Indeed, some good matches have
low and some others high correlation scores, and some false matches have
high correlation scores. This is thus not an acceptable solution if we want

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this process to be universal. Of course, this kind of process can be applied
as a last resort when no particular solutions can be found for each one
of these area problems.
3.3.6 Coping locally with the problems: adaptive window
shapes and sizes
Nicolas Paparoditis
3D data acquisition from visible images 189
The major problem of correlation template/area-based matching techniques
is due to their shape rigidity (square or rectangular) and their fixed sizes.
On the one hand, small templates enable an improved location of the good
matches. On the other hand, larger windows allow a better discrimination
between all possible matches. The problem is that we are confronted
with a classical detection/localization compromise induced by the rigidity
of the templates. Templates’ sizes and shapes should thus change automatically
and adapt themselves according to the changes in the landscape.
We will now explain how this can be done.
Coping with homogeneous areas and periodic structures
For the SMI method and the homogeneous areas, the window size can be
adapted to the local variance of the slave image contents having some
knowledge about the image noise distribution. When areas are homogeneous,
windows will be large, and when the areas are rich in texture,
windows will be small. For periodic structures, we can choose the size of
the template so that the auto-correlation of the texture in its own neighbourhood
along the base line is mono-modal. This would mean that the
texture comprised in the template is no longer a periodic pattern.
These adaptive size techniques are not possible with the SMO method.
Indeed, we would correlate templates of different sizes and this would lead
to heterogeneous correlation scores for all the elevations, thus choosing
the correlation peak could lead to a false match. And it is difficult weighting
the correlation scores according to template sizes. Nevertheless, one can
verify that the templates corresponding to the correlation peak are textured
enough to start, if necessary, another matching process on larger templates.
Another solution is to take a large window of fixed size for all the image
and to weigh the grey-level values by a Gaussian distribution centered on
(i1, j1). The interest of this technique is giving more importance to the
pixels closer to (i1, j1). Nevertheless, if the area is globally homogeneous,
an image feature inside the template window, even if it is relatively far
away from (i1 , j1 ), will allow a possible discrimination in the matching
process. Besides, the estimated disparity will be the one corresponding to
the feature and not to the central point of the template window.

190 Nicolas Paparoditis and Olivier Dissard
Coping with hidden parts
For the SMI method, using the reciprocity constraint is an easy and efficient
way of filtering false matches. We verify that the match of (i 2 , j 2 ),
homologous of (i 1, j 1), is also (i 1, j 1). This process is often called crossvalidation.
This filtering is very discriminating for false matches due to
hidden areas. Indeed, if (i 1, j 1) belongs to a hidden area, it is most probable
that the homologous of (i 2 , j 2 ), estimated as the homologous of (i 1 , j 1 ), will
not be (i 1 , j 1 ).
For the SMO method, we can do a similar process. For the elevation
and the (i 1, j 1) and (i 2, j 2) corresponding to the correlation peak, we can
verify with the SMI method that (i 2, j 2) is the homologous of (i 1, j 1) and
vice versa.
Coping with discontinuities
We can adapt the templates locally if we have a priori information of
where those 3D structures occur. If we do not have any maps, the only
way of obtaining this information is by computing contour maps derived
from the images assuming that a 3D discontinuity is often characterized
in the images by a radiometric contrast. We can locally adapt the template
shapes to the contours so they do not integrate patterns on the other side
of the contours which could be areas at different elevation (Paparoditis
et al., 1998). Cutting the template to produce a mask will of course reduce
the textural content of the template, thus this process can only be carried
out with large enough templates. These kinds of processes are half-way
between area-based and feature-based matching techniques.
With the SMI method, for (i 1, j 1) we limit the template to all the pixels
that are connected to (i 1, j 1), i.e. there is a non-contour crossing path
joining, as shown in Figure 3.3.19(a). If a contour crosses continuously
the template there will be no possible path joining the pixels on the other
side of the contour. If a part of a structure corresponding to a 3D discontinuity
is missing in the contour detection, the adaptive template will be
the classical template itself. A solution is to constrain the path to be straight
lines, as shown in Figure 3.3.19(b). The counterpart of this solution is
that small open contours inside the template will mask all the pixels behind
them and limit the number of pixels intervening in the calculation of the
correlation score. A better solution to take into account those open contours
is to weigh, as shown in Figure 3.3.19(c), all the grey-levels pixels given
by the Figure 3.3.19(a) process by the inverse of the geodetic distance
(Cord et al., 1998) which is given by the length of the shortest path joining
a pixel inside the template and (i 1, j 1).
If (i 1, j 1) is itself on a contour, what should the template be: the right
side or the left side of the contour? Neither in fact, the best solution in
this case is feature-based matching, that is to say matching the contour

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(a) (b) (c)
Figure 3.3.19 In the centre the pixel (i1 , j1 ), in black contours pixels, in grey the pixels belonging to the
adaptive template, in white the pixels which are not taken into account in the correlation
score. (a) template mask with path existence; (b) template mask with straight line paths;
(c) template mask with path existence weighted by the inverse of the geodetic distance.

192 Nicolas Paparoditis and Olivier Dissard
itself. One solution is to look for all the contours in image I 2 along the
epipolar line. Nevertheless, we need to remove ambiguity from all possible
matches by considering the intrinsic information of the contour (we can
verify that the contour orientations are the same) and the geometric and/or
radiometric context around the contour (many solutions are possible). To
add some robustness to this process, we can average, or take the median
value of all disparities for all pixel edges locally along the contour line on
each side of (i 1, j 1) assuming that the disparity is locally stable. These
feature-based matching techniques are often not valid when the contours
are not stable from one image to the other. This is the case for instance
for building edges in urban areas, which are most often not characterized
in the same way in both images.
With the SMO method, we consider the intersection of both image adaptive
template shapes for a given elevation. The interest of this, compared
to that of the SMI method, is that if a part of a 3D contour is missing in
one of the two images, as long as the contours are complementary in both
images this adaptive process will be efficient. Meanwhile this process is to
be carried out carefully, as the number of pixels intervening in the correlation
score calculation change all along the correlation profile.
Coping with geometrical distortions due to slopes
When image quality is good, small templates can be chosen to limit the
distortion effects of sloped relief. In this case we may transform geometrically
the homologous template (when guided from image space) or both
templates (when guided from object space). We can model locally the relief
by a polynomial function of a given order. Then the matching problem
can be seen as finding the optimal set of coefficients giving the highest
correlation score. When the order of the function increases, it is very difficult
finding a robust solution and the process is much longer in time. So
it is preferable to make stricter assumptions on the surface, i.e. supposing
that the surface is locally planar.
Under these assumptions, for the SMI method we can determine for the
square template around (i1 , j1 ) in the reference image, the grey levels of
the homologous template (same size and shape) by intersecting for each
one of its pixels the corresponding 3D ray with a given patch hypothesis
to determine the 3D corresponding point in object space. Given this 3D
point we can determine the corresponding point in I2 and interpolate the
corresponding grey-level value we were looking for and then determine
the corresponding image position and grey level (by interpolation) in the
other image. For all the set of ground patches hypotheses, we can construct
all the homologous templates and thus all the similarity scores. (See Figure
3.3.20, colour section.)
When guided from object space, we can calculate the correlation scores
for all the ortho-templates built for each possible ground patch (z, , )

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Figure 3.3.20 (a) Left image of an 1 m ground pixel size satellite across track
stereopair; (b) right image; (c) DSM result with a classical crosscorrelation
technique; (d) DSM using adaptive shape windows.

194 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.21
x
centred on (X, Y) as shown in Figure 3.3.21, (resp. ) is the angle
between the surface normal and x (resp. y). To limit the search-space
possibilities we can make some assumptions on the maximum slope, e.g.
the slope cannot reasonably exceed 45°. One should remark that implicitly
the 3D entity we are looking for is not the 3D point on (X, Y) but an
entire surface patch around (X, Y).
All these adaptive matching techniques can be mixed together. For
instance, the slope and the 3D discontinuity techniques are to be mixed
together if one wants to determine a 3D measurement of a point on a
sloped roof next to the roof’s edge. The combination of these two techniques
is a strategy guided by the type of landscape to be mapped.
3.3.7 Strategies for a stereopair DSM generation
Nicolas Paparoditis
z
y
O 1 O2
C 1
(X, Y)
We discuss here the strategies of integration of different methods and techniques
to build a regular grid DSM describing the observable surface. We
do not propose an ideal and universal strategy of techniques integration
but different ways of integrating the techniques and the problems related
to their integration. Indeed, the strategy will depend on the type of land-
→
n
→
ds(z, n(α, β))
C 2

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3D data acquisition from visible images 195
scape from natural smooth terrain to complex and dense urban areas, on
the different image resolutions from low to very high, on the data acquisition
conditions, and on image quality, etc. There is possibly a universal
strategy, but it has not yet been found. Even if this strategy exists, some
simpler strategies will be lighter in terms of computing times and efficient
enough for a given set of data on a given landscape.
Basic matching entities and spatial sampling
Can we derive a DEM from a sparse set of 3D points corresponding to
some matched image features entities, i.e. interest points, contour points,
etc. in order to reduce the computing times? The underlying assumption
would be that any relief point could be determined from the nearest 3D
computed features by an interpolation process. Image features are sparse
and do not sample the relief well enough to describe it correctly. Moreover,
these entities are not stable and discriminating enough (especially in the
case of urban scenes) thus leading to ill matches. The denser the entities,
the finer the surface will be sampled. Points or surface patches are thus
the basic matching entities for the DEM matching process even though
image features can help in the process as we will see later on.
In the case of smooth natural relief, surface patches entities seem to be
the most relevant to describe the surface. If we assume the relief to be
smooth enough and planar locally with respect to the size of the patches,
the DEM spatial sampling need not be that of ground pixel size. The DSM
sampling should be constrained by our knowledge of the surface regularity.
In consequence if the surface is smooth the ground size of the surface
patches could be equivalent to the spatial sampling itself. Nevertheless, if
we want the DSM to describe the surface in the most precise way, not
only should the elevation be stored for every DSM grid point. Indeed, for
many applications, the slope information is more or as relevant than the
elevation one. So, the surface patch normal vector could also be stored
for every grid point to improve the precision of both elevation and slope
interpolation processes for a point inside the grid.
For ‘rougher’ surfaces, as in urban areas, a spaced grid of rectangular
shape surface patches would not be adequate as the patches should be
very small to describe the surface correctly. Thus the texture contents of
the corresponding image templates will often not be rich enough to be
entity discriminating. For urban surfaces, we prefer using a denser sampling,
i.e. the process can be carried out for each pixel of image I1 with the SMI
method or for every grid point (X, Y) of the DSM with the SMO method.
In the latter method, the DSM grid spatial sampling should be that of the
size of the smallest objects we would like to represent. Meanwhile, this
does not mean that the spatial resolution of the DSM is equivalent to the
ground pixel size as the measured elevations are a ‘mean’ of all real elevations
inside the template.

196 Nicolas Paparoditis and Olivier Dissard
Initializing the matching process
A gross approximation or knowledge of the surface helps to reduce considerably
the range of the search space intervals to diminish the computing
times and to reduce the matching ambiguities probability. The initialization
strategies are various.
Hierarchical matching
Hierarchical matching processes (Grimson, 1983) first aim at matching a
very restricted subset of image entities i.e. characteristic image features such
as, for example, interest points or contours and use these matches to
initialize the matching of all the other image entities. The matching hypotheses
for all the points lying between the matched features are searched for
in a disparity/elevation search space interval framed by those of the matched
features. This process is efficient when the feature entities are stable.
Using the tie points
A gross surface can be constructed using the tie points that have been used
to determine the relative orientation of the images in the sensor viewing
parameters determination process. The 3D samples corresponding to the
matched tie points can be triangulated to construct a TIN surface that can
be used to initialize the DSM generation. The image can be extremely
dense and thus the gross surface can be quite close to the real surface.
Multi-resolution matching
Multi-resolution matching can be seen as a form of hierarchical matching.
We first build for each image a multi-resolution pyramid as shown on
Figure 2.5.3 using for instance a smoothing kernel filter, e.g. a Gaussian
kernel or a wavelet decomposition. The matching starts from the lower
level of the pyramid, (lowest resolution image) where the disparity vectors
and the range of the search space are much smaller. The surface elaborated
at this resolution is used to initialize the matching at the next step
of the pyramid and so on. The major advantage of this strategy is to lower
in a consequent way the computing times. This matching strategy is valid
when the solution (DSM) provided for a given resolution is close to the
surface observable at the highest resolution. It is thus valid for smooth
surfaces but not for surfaces encountered in urban areas.
Object space vs. image space method
When the matching process is guided from image space, the 3D points
corresponding to the matches of points located on a regular grid in slave

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3D data acquisition from visible images 197
image space have an irregular distribution in object space. Thus the generation
of a spatial regular grid DEM goes through the blind resampling/
interpolation of the irregularly distributed set of 3D samples, which
inevitably leads to artefacts and alters the quality of elevations computed
for all the DEM grid points. It is thus highly preferable determining the
elevations of all the DEM grid points with the SMO method.
As a counterpart, some drawbacks in terms of practical implementation
are to be mentioned. If we generate the DEM by computing the elevations
sequentially for all the points some basic operations are highly redundant,
thus the computing times will unnecessarily increase. Indeed, we mentioned
earlier that the correlation score was applied for a given (X, Y) and for a
given z to the ortho-templates generated by the local resampling of the
images. Neighbouring points in the grid will have for the same z overlapping
ortho-templates. Thus the resampling process for all pixels inside
the overlap will be carried out in a redundant way. And the larger the
windows the higher the redundancy. How can we avoid this? The solution
is to resample both images in object space once for all for a given z.
In other words we build two ortho-images (which have the same geometry
as our DEM) assuming that surface is flat of elevation z. If the relief
around a given (X, Y) is at an elevation z the ortho-templates extracted
from these ortho-images are centred and (X, Y) should be alike. Thus for
this given z and for all the (X, Y) of the DEM grid we can compute all
the correlation scores.
In practice, the determination of the elevations for each DEM grid point
can be done in two ways. The first one consists in initializing the DEM
elevations to the lowest possible z and determining all the correlation scores
for this z and for every point of the DEM grid with our global resampling
and correlation process (we store the correlation scores in a corresponding
buffer grid). For the next possible z we globally process the correlation
scores in the same way. All DEM grid points where the new correlation
scores are higher than those computed with the previous z have their
elevation and correlation scores updated. We continue this process until
we reach the highest possible z. If the storage capacities are limited, we
can cut the global DEM into smaller ones and treat each of them independently
and sequentially. The first interest is that we can verify that the
correlation profile is a good-looking one. The second is that the correlation
profile peak does not always identify the real solution which appears
in the correlation profile as a secondary peak. Keeping all the information
leaves us the possibility of choosing the best solution inside the peak set
with a higher-level processing. This is what we are going to develop now.
Improving the process by looking for a global solution
We have up to now addressed the problem of independent 3D entity measurements.
In the case of dense DEM measurements, we have generated a

198 Nicolas Paparoditis and Olivier Dissard
dense cloud of independent 3D entities that are supposed to describe a
surface. These points should describe a ‘possible’ surface and neighbouring
measurements should be coherent to a certain extent. Indeed, a 3D
measurement cannot be completely decorrelated from its neighbouring
measurements. Even when discontinuities occur their should be a
correlation between all neighbours on each side of the break. We can thus
verify locally or more globally the internal coherence of all the measurements
assuming some modelled hypotheses or constraints on the surface
basic properties.
Detecting erroneous 3D samples
A simple technique often applied to detect erroneous samples is based on
the ordering constraint also called visibility constraint. This constraint,
based on the assumption that the observable surface is a variety in the
form of a single-valued function z f(x, y), verifies (for the SMI method)
that three image points in a given order on an epipolar line also follow
the same ordering on the conjugate epipolar line.
This constraint can also be applied, in object space, to the surface
samples. Indeed, every 3D sample has been determined by matching homologous
points thus supposing implicitly that these points are visible in both
images. We can thus verify, with a z-buffering algorithm, that every 3D
sample is directly visible in both images and not hidden by any other
3D samples. If some samples are hidden we have some evidence of the
existence of erroneous samples. As shown in Figure 3.3.22 there is an
obvious incompatibility between P1 and P2. P 1 or P 2? O 1 O 2 P 2
C 1
P 1
Figure 3.3.22 Mapped surface incoherence detection.
P 2
C 2
H

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In the case of natural relief, we can verify that the surface is locally,
smooth, planar and continuous. For a 3D patch process, we can verify
that neighbouring 3D patches are connex. If one of the patches is not at
all correlated with its neighbours, the patch is discarded and can be replaced
by a patch fitting with the neighbouring ones. For a 3D point process, we
can determine a plane fitting locally the 3D neighbour samples by a least
squares estimation technique and verify that the considered point is close
enough to this plane. We can still manage this process if a discontinuity
occurs assuming that this discontinuity is characterized by a contour in
one of the images. Indeed, we can transpose the 3D samples in image
space and we can consider only the neighbouring samples that are on the
same side of a contour. Besides, if a local connected set of 3D entities is
erroneous, i.e. the errors are structured and spread, this process rejoins
the ill-posed problems.
Finding the best 3D surface in a global way
A ‘clean’ solution to find the most ‘probable’ surface is keeping for all the
entities all or a subset of the best (the highest correlation peaks) matching
hypotheses and finding the best path or surface fitting the ‘fuzzy’ measurements
by an optimization technique. We can evaluate the realism and the
‘probability’ of each possible path and retain the best one given a cost
function integrating constraints on the surface behaviour. Figure 3.3.23
z
C 1
O 1
O 2
Structured erroneous hypotheses
C2 1st best match peak
2nd best match peak
3rd best match peak
x
best ‘fuzzy’ path
path given by the best
matching hypotheses
Figure 3.3.23 A virtual example of possible path optimization of the best 3D
samples hypotheses given by the SMO method. In black we have
the path given by the independent best matching hypotheses.
In dotted line, we have the best ‘fuzzy’ path assuming some
constraints, i.e. the surface is continuous and smooth with no steep
slope.

200 Nicolas Paparoditis and Olivier Dissard
shows an example of a global optimization with a continuity constraint
where we have kept for each (X, Y) along a 3D ground profile, the three
most probable z values corresponding to the three highest correlation peaks
obtained with the SMO method.
The optimization techniques that can be applied are numerous, i.e. relaxation,
least squares, dynamic programming, etc. We will not describe these
techniques here, one can find them in any good signal or image processing
book. What differentiates these techniques is the domain on which the
optimization is carried out. Relaxation is usually applied to small neighbourhoods
around the samples. Dynamic programming is applied to
samples along linear ground (as shown in the example of Figure 3.3.23)
or image (e.g. epipolar lines) profiles. The larger is the domain, the higher
are the chances of finding a ‘correct’ global solution but the higher is the
optimization complexity and the computing times. Besides, if we choose
local domains, we have to ensure that all the connected domains are
coherent thus leading us to another optimization problem.
The optimization processes can be carried out in the same way in the
object space, i.e. on the 3D samples hypotheses or in image space on the
matching hypotheses. One of the major interests of these processes besides
improving globally the results is that we can use windows of smaller sizes
and have a better local and morphological rendering of small 3D structures.
Moreover, using the windows that are as small as possible is a
guarantee that the neighbouring measurements are the ‘more’ independent
as possible thus lowering the probability of having structured erroneous
areas that could mislead the optimization process.
When the surfaces are not continuous but piecewise continuous as in
urban areas, the optimization process should take into account the location
of the 3D break lines to authorize locally a depth or a disparity
discontinuity. As we do not have any a priori information on their 3D
location, the only information we can inject in the process is the location
of image contours, which are the projections of possible 3D breaks (March,
1989). We can then apply a continuity constraint on the hypotheses
(brought back in image space) on each separate side of the contour. As
we said earlier, in urban areas, contours corresponding to building limits
do not appear in all the images at the same time, but most of the time a
given building edge appears contrasted in at least one of the images. Thus
if we want the break process to be efficient we have to consider the optimization
on all the contours of all the images at the same time. Nevertheless,
one should have in mind that this process can in some cases generate
virtual depth discontinuities around non-3D contours.
Figure 3.3.24 An example of the management of hidden parts(a): in (b) the left
image; (c) the raw DSM, with (in black) the areas where the correlation process
failed. Considering that these zones are generally on the ground, by subtracting
the DTM (e), obtained by smoothing the data acquired between the raised
structures, one gets a DEM (d) with only minor imperfections.

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(a)

202 Nicolas Paparoditis and Olivier Dissard
It is necessary to discard, before the optimization process, all the grid
points that have no significant correlation profile. Indeed, these points
could correspond to areas that are hidden due to occluding structures. Thus
looking for a path in these areas would have no sense and would lead in
all cases to an erroneous solution. Should these points be a posteriori
blindly interpolated in the DEM generation process? Certainly not! This
would lead us to odd-looking surfaces. The hole-filling strategy should be
decided and guided by the operator. The alternative solution if we desire
a fully automatic process would be to have the existence of a solution
inside the matching hypotheses for every landscape point. This means that
every landscape point should be seen in at least two images of the survey.
In the case of urban surveys, this implies a high stereo overlap (along and/or
across-track). The optimization process should then be carried out on all
the 3D sample hypotheses accumulated from all the possible stereopairs
(Roux et al., 1998). Another alternative is to consider that missing
areas are on the ground. Identifying and removing all the raised structures
through a joint image/analysis will leave inside the DSM only the ground
elevation samples. Thus the elevation values for the initial missing areas can
be interpolated from all the set of ground elevation samples. (See Figure
3.3.24, colour section.)
3.3.8 An example of strategy for complex urban landscapes:
dynamic programming applied to the global and
hierarchical matching of conjugate epipolar lines
Olivier Dissard
We will describe here a global matching process based on dynamic
programming that integrates contours to model the 3D discontinuities.
This scheme (Baillard and Maître, 1999; Baillard and Dissard, 2000) has
given very good results on urban, suburban, and rural landscapes.
What is dynamic programming in the case of epipolar images
matching?
For the purpose of stereo image matching, dynamic programming should
be considered as the search for the ‘best’ path between two known pairs
of homologous points, to derive the 3D profile between these two points.
‘The best’ is considered in relation to an energy function that assesses the
resemblance between each of all the possible pairs of points.
Considering the SMI point of view, epipolar resampled images represent
an interesting workspace: considering each pair of homologous lines,
the aim becomes to search for a ‘best’ path between the two origins and
ends (or two known pairs of homologous points) in the space defined by

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3D data acquisition from visible images 203
the right and left epipolar lines and filled with a similarity function (see
Figure 3.3.25). All the explanations that follow are based on a ‘pixel-topixel’
but not a sub-pixel matching.
Similarity function
A necessary condition for the similarity function is that the computation
must be comparable everywhere: for example, adaptive windows for the
computation of cross-correlation coefficient do not provide comparable
values because the height of the correlation peak depends on the size of
the window. Some computation tricks reduce the influence of window size
without solving it. Thus, in these cases there can not be an objective optimized
path.
The similarity assessment used for the matching in Figures 3.3.25 and
3.3.26 is nothing but the simple cross-correlation coefficient on a neighbourhood
with constant size. It does not assess the resemblance of the
local radiometry, but the resemblance of the radiometry change inside the
neighbourhood. We will see later how to take radiometric resemblance
into matching with dynamic programming.
Possibilities for paths
On the assumption that objects on both epipolar lines should be found in
the same order (which is quite the reality, except mobile objects or perspective
effects on lateral sides of the epipolar pair between pylons or trees
and ground texture), each possible path that goes through a point comes
from only three directions (Figure 3.3.25). It means in fact that there is
no possibility of going back on one image when going forward on the
m–1
m
Right epipolar line
n–1
2
3
n
1
Left epipolar line
Figure 3.3.25 Possible paths for matching with epipolar lines.

204 Nicolas Paparoditis and Olivier Dissard
other one. This simple but quite robust assumption makes the computation
possible, for the best path through a point derives from three best
paths with coordinates less than or equal to the considered ones.
The selected path on the point P(n, m) is then:
P(n, m) Max(P(n, m1) Energy(1), P(n1, m1)
Energy(2), P(n1, m) Energy(3)). (3.16)
Let us examine each path:
• Path 2 means that the disparity of (n, m) is the same as the disparity
of (n1, m1): we are on a horizontal 3D surface.
• Path 1 means that we have moved one pixel forward on the right
image, keeping the same position on the left one, disparity has
progressed. If (n, m) belongs to the right path, it means that we are
on a part of the right image that does not appear on the left one:
occlusion, mobile vehicle, specularity, etc.
Path 1 is also for sloped areas: for example, a 1 ⁄2 sloped profile will
alternate Path 1 and Path 2 through the optimized path.
• Path 3 is the opposite of Path 2, regarding left and right lines.
Into the algorithm, point (n, m) will be assigned with the value of P(n, m)
and O(n, m) which is the provenance (1, 2 or 3) of P(n, m):
O(n, m) Arg(energy) (Max(P(n, m1) Energy(1),
P(n1, m1) Energy(2), P(n1, m) Energy(3))).
(3.17)
Thus P is used for progressing from the beginning point to the end point,
while O allows going back to the beginning point, once the end point is
reached.
Energy function
Let us consider Path 2: it means that disparity is the same between (n, m)
and (n1, m1), in other words, it means that the 3D profile is continuous,
the homology between points n and m is acceptable, therefore the
similarity function must provide an acceptable value.
Considered from an opposite point of view, we will assume that Path 2 is
the right one if the similarity function (the correlation coefficient cc(n, m))
is acceptable, higher than a given threshold ccmin. Path 2 cc(n, m). (3.18)

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3D data acquisition from visible images 205
What happens when cc(n, m) Path 1 Path 3.
cc min
Thus Path 1 Path 3 (3.19)
2 .
Application
Figure 3.3.27 shows two epipolar lines, a correlation coefficient matrix,
and the optimized path between beginning and end points. This algorithm
is very convenient for urban context where one usually has to deal with
continuous 3D areas, mixed with disparity gaps due to vertical façades.
Mobile vehicles, or opposite contrasts due to specular reflection are overcome
with series of ‘Path 1 Path 3’. However, the algorithm is robust,
for it finds the right path very quickly after such accidents.
Finally the optimized path is ‘symmetric’: the paths are the same if we
go from ‘end’ point to ‘beginning’ point.
There is no necessity in having homologous pairs of points as beginning
and end points, because the incidence is in fact very limited; the right path
is always directly found after the right number of Paths 1 or Paths 3.
Intervals of search can be limited to reduce computation time, for
example with a map of 3D contours: the beginning point is a 3D contour
C1(n1, m1) and the end point is the next one C2(n2, m2): the optimized path
has a length L < n2 n1 m2 m1. Forbidden paths: how to introduce new constraints
For different reasons, some pairs of points cannot be matched. It is
expressed on the matrix by parts or points, through which every Path 2
has a very low energy: instead of computing the correlation coefficient on
these points, we decide that cc

Forbidden area:
Heights > DTM
Right epipolar line
Figure 3.3.26 Restriction of the space search.
Left epipolar line
Forbidden area :
DTM + maximum
height above ground
Figure 3.3.27 Correlation matrix corresponding to the matching of the two
epipolar lines appearing in yellow in the image extracts.
Every grey level with coordinates. (i, j) in this matrix corresponds to the correlation score
and the likelihood of the matching hypothesis between pixel of row number i along the
epipolar line in image 1 and pixel of row number j along the epipolar line in image 2. The
best path found with the dynamic programming within the correlation matrix is superimposed
in yellow. The red lines show some examples of corresponding points found along the path.
The green lines and areas show, respectively, some examples of 3D occultation contours and
the corresponding occluded area in the other image.

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3D data acquisition from visible images 207
radiometric modelling. The examples in Figures 3.3.28 (colour section),
3.3.29 and 3.3.30 are obtained with such a two-step algorithm.
Some parts are forbidden even for occlusion, for example in the case
where we know lower and higher possible altitudes (with a coarse matching,
or by the knowledge of a DTM and a maximum height of the aboveground
objects – trees or buildings). Restriction of the search space greatly
speeds up the process (see Figure 3.3.26).
What matching difficulties does dynamic programming solve
and not solve?
This algorithm is conceived to solve the matching difficulties due to aboveground
vertical façades, and in fact, it solves the problem of mobile vehicles,
when no matching ambiguity appears. Repeated textures, such as parking,
are also solved by dynamic programming, considered as global optimization.
To the contrary, this algorithm suffers from the similarity measure that
takes contrast into account, and thus the borders of 3D objects are unlocalized
with an error equal to the radius of the measure neighbourhood.
There are still matching ambiguities: a mobile vehicle matched with a
parked one – see Figure 3.3.30, confusion with objects on buildings’ walls
occluded on one image, etc.
One can find more details in Baillard and Dissard (2000). Also, see
Figures 3.3.27 and 3.3.28 (colour section).
Figure 3.3.28 Results of the global matching strategy on a complete stereopair
overlap in a dense urban area. The yellow line superimposed on
the two images corresponds to the line we have matched previously
in Figure 3.3.27.

208 Nicolas Paparoditis and Olivier Dissard
3.3.9 Improving the DEM generation in urban areas with
higher quality data: multiple views and digital images
Nicolas Paparoditis
At these levels of resolutions and in a context of dense urban tissue, there
are a considerable number of hidden parts to the extent that a dense and
thorough description of the scene by a stereo analysis is limited (Figure
3.3.29). Besides in urban areas, the classical stereo processing admits some
flaws due to all the matching ambiguities encountered, e.g. mobile vehicles
(Figure 3.3.30), repetitive structures and also due to the poor image
quality. Poor image quality for instance in scanned images is due to noise
added by the scanning process, to the dust, the scratches, and other dirt
present on the silver halide photographs, but also due to the non-linearity
of the silver halide sensibility. Indeed, the signal to noise ratio is dreadful
in dark areas such as shadows, which will thus have poor chances of being
matched if they are hard.
Digital images
The quality of the images, i.e. the signal to noise ratio, is the key factor
for the quality of the products that can be derived from these images.
Figure 3.3.29 Missing information in the DSM due to the hidden areas in the
images especially areas around building ground footprints.
Figure 3.3.30 Artefacts due to mobile vehicles. Indeed the stereo-process supposes
that the observed surfaces are still between the two acquisitions.

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3D data acquisition from visible images 209
Indeed, with a digital imaging system with a much higher signal to noise
ratio, the image content within ‘homogeneous’ areas and shadowed areas
is still quite rich, nearly as much as the rest of the image (with just a lower
signal to noise ratio), and will still be fully exploitable. This is a completely
different situation from what happens in classical silver halide pictures,
even if the digitization has been performed with the best possible performances.
(See Figures 3.3.31 and 3.3.32.)
Figure 3.3.31 Impact on homogeneous areas of a higher signal to noise ratio.
For the same building and pixel size: (a) digitized image with
(b) image processing. In (c) CCD digital image (IGN-F camera),
with (d) image processing.
Figure 3.3.32 One can see the poor image content (a) within the shadows due to
the poor sensibility of the film within the dark areas in comparison
with the rich shadow contents (b) inside the digital image thanks
to the sensibility and the linearity of the CCD sensor. These images
were taken at the same time thus in the same lighting and
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210 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.33 Index map of a 60 per cent along track and across track overlap
digital survey on the French town of Amiens.
Multiple views
The acquisition of surveys with multiple views (a particular spot of the
landscape is seen in more than two images) solves many problems. Actually,
provided a sufficient overlapping between images exists, there will always
be one or more couples among the whole set of couples in which a given
point of the landscape is visible and where some of the problems described
previously, e.g. mobile vehicles and non-Lambertian surfaces, will not
appear. In the case of Figure 3.3.33, one landscape point can be seen in
up to 9 images, thus in up to 36 along or across track stereopairs made
out of these 9 images.
Multiple views: merging elementary DSMs processed on all
stereopairs
Means of exploiting this data have been largely treated in recent literature
(Canu et al., 1995; Roux et al., 1998). In most of the techniques, the
general idea is to reconstruct the DSM by an a posteriori merging of all
the elementary DSM calculated on all the possible stereopairs by a voting

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3D data acquisition from visible images 211
Figure 3.3.34 (a) (b) (c) Three elementary stereopair DSM on the same scene.
One can notice that the hidden areas are not located at the same place; (d) DSM
obtained by merging the three elementary DSMs.
Figure 3.3.35 Zoomed extracts of the DSMs appearing in Figure 3.3.32.
technique (e.g. based on the median value). This merging allows a
densification and reliabilization of the results to a large extent when the
elementary DSM are complementary and when the results are valid in
most of all the DSM. (See Figures 3.3.34 and 3.3.35.)
The stereo matching process requires the use of non-negligible window
sizes if one is looking for sufficiently reliable measures. One knows well
that the morphological quality of the DSM, i.e. the ability to render discontinuities,
slopes, slope breaks, surface microstructures, all of utmost
importance for numerous applications, is directly dependent on the window
size. The larger the windows and the more the ‘high frequencies’ of the
surface are smoothed out, the more the depth discontinuities are delocalized,
and the more the matching of steep slopes is difficult (due to image
deformations). (See Figure 3.3.36.)
One way to reduce the window size is the signal to noise ratio of the
images so as to reduce matching ambiguities. This can be obtained naturally
by having an imaging system of higher quality, or artificially by increasing
the number of observations.

212 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.36 DSM with superimposition of the real roof building edges. One can
see the delocalization of the building depth discontinuities.
Generating the DSM with all the images at the same time: a
multi-image matching process guided from object space
A process based on the concept of direct multi-image matching guided
from object space can be used to process all the images at the same time
to generate the DSM (Figure 3.3.37) (Paparoditis et al., 2000). This process
allows the matching of the images and the construction of the raster DSM,
and the orthoimage all at the same time without having to go through the
processing of all stereopairs and the merging of all elementary DSMs.
The process is based on the following algorithm. For every single node
(x, y) of the DSM raster grid, a correlation profile is constructed gathering
all the correlation scores calculated for each of the possible z through a
plausible interval [zmin, zmax] depending on an a priori knowledge of the
scene (given by a map, a gross DTM, etc.). For each given z, one calculates
in the whole set of images, the hypothetical corresponding (ik , jk )
image coordinates in each image space k (where 0 < k < n and n is the
number of images where this (x, y, z) point is seen). The likelihood of these
hypotheses is given by a direct measurement of the similarity of the set of
windows centred on the (ik , jk ). The ‘estimated’ z value retained for a given
(x, y) is the one for which the optimal value of the correlation profile is
reached. Besides, for this (x, y) and for this estimated z we can calculate
directly the corresponding grey level in the orthoimage from the set of
associated (ik, jk) grey levels by taking for instance the average or the
median of the values.
A multi-image similarity function
How can one generalize the similarity function to a set of image windows?
By defining for example a criterion describing the collinearity dispersion

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3D data acquisition from visible images 213
Correlation profile
Figure 3.3.37 Multi-image matching guided from object space.
C
C
of all texture vectors corresponding to all template windows. One can do
this by using this new multi-image texture similarity (MITS) function:
Var
0 MITS (i1, j1, i2, j2, … , in, jn)
n
k1
n
n ,
Var (Vk(i k, jk)) k1
V k (i k ,j k )
(3.20)
where V k (i k , j k ) is the texture vector associated to the window centred on
the pixel (i k , j k ) in image k and Var(V k (i k , j k )) the variance of the texture
vector V k (i k , j k ), i.e. the grey levels inside the window centred on the pixel
(i k , j k ) in image k. Why this correlation function? If the image texture
windows are alike, i.e. the texture vectors are collinear, the similarity score
is maximal.
A radiometric similarity weighting
In view of the great radiometric stability of digital images (which is not
the case of scanned images) and under the assumption that most of the
objects that describe the landscape have Lambertian characteristics, we
z
z max
z
z min

214 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.38 Comparison of homologous windows (3 × 3) found for a given
(x, y) point without and with the radiometric weighting function.
impose an additional constraint on the absolute radiometry of homologous
neighbourhoods, in the shape of a weighting function. This weighting
is necessary. Indeed, the MITS similarity function is ‘centred average’. This
function measures the similarity of the textures of all neighbourhoods but
not their radiometric similarity; this can give rise to mismatches. Our new
similarity function called MITRAS (multi-image texture and radiometric
similarity) can be expressed in the following way:
MITRAS (i 1, j 1, … , i n, j n)
, (3.21)
k
where: Var is the variance, Im (i, j) the grey level of pixel (i, j) in image Im ,
and k a normalizing coefficient. The application of this weighting function
permits a similarity criterion to be obtained which characterizes at
the same time the texture and the radiometric resemblance of the neighbourhoods.
Therefore the MITRAS similarity function is more robust and
discriminating (Figure 3.3.38).
MITS (i 1 , j 1 , … , i n , j n ) exp Var k (I k (i k , j k ))
Multiple view DSM results and window size impact
The increase in the number of observations allows on the one hand a
sizable reduction of matching ambiguities met with in the classical stereoprocessing
and thus to increase the reliability of the process. On the other
hand, it allows, also thanks to the high quality of digital images, sizes for
the correlation windows of 3 × 3 to be used (Figure 3.3.39). The results
show clearly a dense DSM, an extremely good morphological rendering:
all relief slopes, slope breaks, discontinuities and microstructures, and a

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Figure 3.3.39 DSM generated with 4 images and 3 × 3 windows.
Figure 3.3.40 DSM generated with 4 images and 5 × 5 windows.

216 Nicolas Paparoditis and Olivier Dissard
good localization of the discontinuities (especially the building edges).
However, the very small size of the windows is at the origin of false
matches in the very homogeneous areas that do not appear with a 5 × 5
window (Figure 3.3.40). To the contrary, a 5 × 5 window has a less accurate
rendering of microstructures and discontinuities.
Working from object space offers a good number of advantages. One
can work in a transparent way on images of different resolutions, and the
parameters are expressed in a metric form. Also we avoid the blind resampling
of all the 3D samples corresponding to all image matches in order
to generate a regular grid DSM in object space. Indeed, these samples
when the matching process is guided from image space follow, although
their distribution is regular in image space, an irregular spatial distribution
in object space. Finally, its major advantage is that it allows, on the
Figure 3.3.41 Orthoimage corresponding to the DSM of Figure 3.3.40. Images
with 40 cm ground pixel size from the digital camera of IGN-F on
the French town of Le Mans with a 50 per cent across and along
track overlap.

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3D data acquisition from visible images 217
Figure 3.3.42 2,000 × 2,000 Raw DSM obtained with our process on 4 images
and 3 × 3 windows.
one hand N images to be treated in a natural and transparent way, and
on the other hand, the DSM and the corresponding orthoimage to be
constructed at the same time.
Matching self-evaluation and automatic filtering of false
matches
As expected, the multi-image correlation score does not supply a probability,
but a good self-indicator of the measurement reliability. The results
(in Figure 3.3.42 and Figure 3.3.43) show that DSM aberrant points have
much weaker correlation scores.
A simple experiment of analysis of the correlation score distributions
shows this very clearly. Let us consider real and aberrant score distributions.
We call real scores those found with our process, and aberrant scores
those obtained by the same process with the proviso that one deliberately
stands within an altimetric search interval of the same amplitude but
containing no relief. One can observe that the two distributions are

218 Nicolas Paparoditis and Olivier Dissard
Figure 3.3.43 Correlation scores corresponding to Figure 3.3.42.
0.000
0.230
0.460
0.690
0.920
1.150
1.380
1.610
1.840
2.070
2.300
MITRAS on 4 images
2.530
2.760
2.990
3.220
3.450
3.680
3.910
Figure 3.3.44 Correlation score histograms.
real matches with 5×5 window
real matches with 3×3 window
false matches
but slightly mixed (Figure 3.3.42). From an inspection of the curves, it
can be said that on this scene the points having correlation scores above
2.9 are almost 100 per cent sure. (See Figure 3.3.44.)
The relative distribution separation in the case of multi-image matching
allows a valid criterion for false points filtering to be defined. It can be
noticed that the greater the number of images, the greater is the separation
of the two distributions. In the case of stereo-processing, the mixing

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3D data acquisition from visible images 219
Figure 3.3.45 DSM of Figure 3.3.42 filtered with a 2.9 threshold on the
correlation scores of Figure 3.3.42.
of the distributions is considerable. This explains the difficulty and the
impossibility of defining a reliability criterion and a satisfying rejection
threshold on the correlation score values. A low threshold retains a great
number of aberrant points, while a high one rejects a very great number
of valid points. (See Figure 3.3.45.)
This matching process tends voluntarily to determine solely the landscape
points seen in a rather similar way on all the images. As a result,
the filtering process will remove all other points and leave missing areas
inside the DSM. For example surface points that are only seen in a subset
of images will be removed. Nevertheless, we have here the first step of a
general matching strategy that can be to complete in a progressive and
hierarchical way the DSM starting from the most reliable measures.

220 Nicolas Paparoditis and Olivier Dissard
3.3.10 Generating a DTM from a DEM: removing buildings,
bridges, vegetation, etc.
Nicolas Paparoditis
In the case of dense urban areas and extended areas of vegetation, even if the
stereo-process is carried out on SPOT like low-resolution images, the
measured elevation samples will describe the rooftops and the canopy
surface. The only proper way of generating a DTM from a DEM is by removing
from the DEM all the samples corresponding to 3D raised structures, i.e.
vegetation, buildings, etc. and fitting surfaces through the holes. This process
requires a 3D analysis of the DEM, which can be combined with an image
analysis to detect and recognize all these cartographic features.
References
Baillard C., Dissard O. (2000) A stereo matching algorithm for urban digital
models, Photogrammetric Engineering and Remote Sensing, vol. 66, no. 9,
September, pp. 1119–1128.
Baillard C., Maître H. (1999) 3D reconstruction of urban scenes from aerial stereo
imagery: a focusing strategy, Computer Vision and Image Understanding, vol. 76,
no. 3, December, pp. 244–258.
Bertero M., Poggio T., Torre V. (1988) Ill-posed problems in early vision, IEEE
Proceedings, vol. 76, no. 8, pp. 869–889.
Canu D., Ayache N., Sirat J.A. (1995) Accurate and robust stereovision with a
large number of aerial images, SPIE (Paris), vol. 2579, pp. 152–160.
Cord M., Paparoditis N., Jordan M. (1998) Dense, reliable and depth discontinuity
preserving DEM computation from H.R.V. images, Proceedings of ISPRS Commission
II Symposium, Data Integration: Systems and Techniques, Cambridge,
England, July, vol. 32, no. 2, pp. 49–56.
Gabet L., Giraudon G., Renouard L. (1994) Construction automatique de modèles
numériques de terrain à haute résolution, Bulletin SFPT, no. 135, pp. 9–25.
Grimson W. (1983) An implementation of a computational theory of visual surface
interpretation, Computer Vision Graphics Image Processing, no. 22, pp. 39–69.
March R. (1989) A regularization model for stereo vision with controlled continuity.
Pattern Recognition Letters, no. 10, pp. 259–263.
Okotumi M., Kanade T. (1993) Multiple Baseline Stereo, IEEE Transactions on
Pattern Analysis and Machine Intelligence, vol. 15, no. 4, April, pp. 353–363.
Paparoditis N., Cord M., Jordan M., Cocquerez J.P. (1998) Building detection and
reconstruction from mid to high resolution images, Computer Vision and Image
Understanding, 72(2), November, pp. 122–142.
Roux M., Leloglu U.M., Maître H. (1998) Dense urban DEM with three or more
high resolution aerial images, ISPRS Symposium on GIS, Between Vision and
Applications, Stuttgart, vol. 32, no. 4, September, pp. 347–352.
Tikhonov A.N. (1963) Solution of incorrectly formulated problems and the regularization
method, Soviet Mathematical Document, no. 4, pp. 1035–1038.

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3.4 FROM THE DIGITAL SURFACE MODEL (DSM) TO
THE DIGITAL TERRAIN MODEL (DTM)
Olivier Jamet
As soon as one is interested in the topographic data production with a
rms accuracy in altitude of the order of a metre or less, the derivation of
a DTM from the calculated DSM, by manual edition or automatic levelling
of the raised structures, is an indispensable step. The semi-automatic
processes permitting one to alleviate the edition of the DSM can be classified
in three categories.
3.4.1 Filtering of the DSM
From the DSM to the DTM 221
Techniques of filtering are based on the hypothesis that elements of the
raised structures constitute connex zones of limited area and presenting
strong contrasts of elevation with their environment. The method most
often used is issued from mathematics morphology: the DTM is obtained
by morphological opening of the DSM by a structuring element defined
by its size and its geometry (parameters of the filter). This method is
perfectly rigorous only in a plane land. Indeed it doesn’t preserve the curvature
of the land. The quality of the DTM produced will be therefore worse
if the land is hilly and if the structuring element is of large size. Besides,
the abrupt irregularities of the land leads to artefacts that can become very
visible for openings of large size, as in the case of the elimination of
building envelopes in a metric resolution DSM, for example. These artefacts
can be accentuated by the noise of the DSM, and more precisely by
the presence of local parasitic minima. A filtering of these local minima,
for example by an applied morphological closing of the DSM, will then
improve the results.
A variant of this method of levelling of the raised structures consists in
applying openings of increasing successive sizes with structuring elements
of variable shape up to the wanted size. If this method doesn’t preserve
the accuracy of the DTM better in the presence of strong curvatures, it
has the advantage of producing a smoother result.
3.4.2 Segmentation and elimination of the raised structures
An alternative to the simple filtering consists in using techniques of shape
recognition to circumscribe the extension of the raised structures. The
DTM is then calculated by replacing, on the extension of the detected
raised structures, the initial elevation values by interpolated values. This
segmentation of the raised structures can be done by a process of the DSM
only, or by analysing jointly an orthophotography of the same zone.

222 Olivier Jamet
3.4.2.1 Segmentation of the DSM
All tools of segmentation used in picture analysis can obviously be used
for the analysis of the DSM, requiring a definition of the criteria characterizing
the raised structures in relation to the ground.
The simplest methods are based on the examination of slopes or curvatures
of the DSM for a detection analogous to a detection of contour in
an image. The selection of the raised structures in the extracted contours
is made by imposing that contours are closed and that the value of the
slope on contours is greater than a minimal value. A supplementary
constraint on the size of the detected zones can also be applied. These
techniques are not recommended. They will always be extremely sensitive
to the accuracy of the DSM at the edge of the raised structures, though
this accuracy is impossible to guarantee (either because of qualities of the
picture having served to the extraction, or because of the hidden parts in
the case of a matching on a couple of pictures).
It appears therefore preferable, if one uses only elementary operations
of image process, to use the method described in §3.4.1. A simple threshold
on the difference between the DSM and the DTM produced by morphological
opening will indeed give a segmentation of the raised structures
a priori more reliable than techniques of contour extraction – this
segmentation permitting the calculation of a new DTM by initial data
interpolation.
To palliate the fragility of methods based on contour extraction on the
DSM and the shortcomings of methods based on mathematical morphology,
which will fail systematically in cases of extended raised structures
(islets of buildings in urban zone, forests, etc.) and hilly landscapes, some
more elaborate methods are made the object of research. In Baillard (1997),
the raised structures is defined by a Markovian model in which the labelling
of a region as raised structures is a function of relations of dependence
with its neighbouring regions (e.g. ‘a zone higher than a neighbouring zone
recognized as belonging to the raised structures necessarily belongs to
the raised structures’). Methods of segmentation by area growth, with a
criterion of homogeneity based on differences of altitude between neighbouring
points are proposed also in Masaharu and Hasegawa (2000), and
Gamba and Casella (2000) for example. Other authors use some cartographic
data to force the segmentation (e.g. Horigushi et al. (2000)). (See
Figure 3.4.1, colour section.)
3.4.2.2 Segmentation of an orthophotography superimposable
on the DSM
The interpretation of photographic pictures of the studied zone, if not alone
able to distinguish the raised structures without ambiguity, can improve the
reliability of processes of segmentation of the DSM. In particular, specific

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detectors (recognition of the structure, vegetation) applied on an orthophotography
superimposable on the DSM will provide complementary masks
combinable with the segmentation of the DSM. Dissard applies this technique,
for example, for the detection of forest zones.
3.4.3 Selection of ground points in the DSM
From the DSM to the DTM 223
Figure 3.4.1 Images from the digital camera of IGN-F (1997) on Le Mans
(France). The outstanding signal/noise ratio allows one to get
excellent matching results on the automatic correlation process,
particularly on homogeneous or shadowy zones where normal
digitized images always produce many difficulties. Benefit is taken
from this situation, by using small correlation windows (5 × 5 and
even 3 × 3), which improves the planimetric accuracy.
A third approach consists in selecting, by an ad hoc procedure, a set of
points situated on the ground in the DSM, and rebuilding the DTM by
interpolation of this set of points. This technique has the advantage of
avoiding the problem of an exact segmentation of the extensions of the

224 Olivier Jamet
raised structures. It can, however, be used only in the individual cases
where the strategy of selection of ground points is very reliable (the sensitivity
to errors being as large as the density of the selected seeding is low).
It is, for example, the case in urban zones, when the land varies little.
One can be content with a scattered set of points, which one can choose,
for example, on the road network (if a cartography is available, or while
calculating an automatic extraction).
In the absence of other information, it is also possible to use procedures
of blind selection of local minima in an analysis procedure of the DSM
by mobile window, the window of analysis being chosen of sufficient size
not to be ever entirely covered by the raised structures. This method,
however, is rigorous only in flat landscapes and is extremely sensitive to
the noises of the DSM.
3.4.4 Conclusion
These methods cannot be considered as perfectly operative, however.
Only the simplest algorithms (as algorithms of filtering that are most
current) are generally present on digital photogrammetric workstations.
They will give most of the time good results on landscapes of moderate
slope and when the raised structures is constituted of connex parts of weak
extension. They remain therefore precious from the moment the number
of these connex parts is high, because they will allow one to save a lot of
editing time.
They are, however, very sensitive to the quality of the calculated DSM,
and in particular to the slope of the DSM at the borders of the raised
structures (that must be the strongest possible). They can also produce
some unexpected results on ambiguous superstructures such as bridges,
which can either be considered as belonging to the raised structures or
not. They must not therefore be used without supervision.
References
Baillard C. (1997) Analyse d’images aériennes stéréoscopiques pour la restitution
3D des milieux urbains: Détection et caractérisation du sursol. Ph.D. Thesis,
École Nationale Supérieure des Télécommunications, Paris.
Horigushi S., Ozawa S., Nagai S., Sugiyama K. (2000) Reconstructing road and
block from DEM in urban area, Proc. ISPRS Congress 2000, International Archives
of Photogrammetry and Remote Sensing, vol. XXXIII, Part B3, pp. 413–420.
Gamba P., Casella V. (2000) Model independent object extraction from digital
surface models, Proc. ISPRS Congress 2000, International Archives of Photogrammetry
and Remote Sensing, vol. XXXIII, Part B3, pp. 312–319.
Masaharu H., Hasegawa H. (2000) Three-dimensional city modelling from laser
scanner data by extracting building polygons using region segmentation method,
Proc. ISPRS Congress 2000, International Archives of Photogrammetry and
Remote Sensing, vol. XXXIII, Part B3, pp. 556–562.

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3.5 DSM RECONSTRUCTION
Grégoire Maillet, Patrick Julien, Nicolas Paparoditis
3.5.1 Digital elevation models under TIN shape
Grégoire Maillet
DSM reconstruction 225
The natural form of the DEM is raster (a regular grid of altitudes), either
acquired by correlation or by laser scanning. But, given their extremely
heterogeneous nature and the presence of discontinuities, this format is
neither adapted to their storage nor to their manipulation. The construction
of a TIN (for triangulated irregular network) presents the two favourable
features to reduce greatly the volume of data (a reduction of around 90 per
cent for an urban DEM) and to be more effective for all applications of
visualizations [1] (Figure 3.5.1.5). Besides, this construction is a first raw
data interpretation that may facilitate the analysis of the scene [2].
Contrary to the general problems of surface triangulation, the raster origin
of data makes it possible here to work in 2.5D. Most of the existing
methods are based on the recursive insertion of points in a planimetric triangulation
up to the satisfaction of a criterion on the number of points or
on the quality of the approximation [3]. The problem can be decomposed
therefore into two independent sub-problems: the way to triangulate points
and the criterion of the choice of the points to insert.
A triangulation by a simple splitting into three of the triangle to the
vertical of the point to insert leads inevitably to triangles of very acute shape
that are very difficult to manipulate. The criterion of Delaunay allows the
appearance of these problems to be minimized, and there are very efficient
implementations of insertion of points in a Delaunay triangulation [4][3].
Nevertheless, the lack of taking into account the altitude can lead to optimal
triangulations in planimetry, but disjointed in 3D (Figure 3.5.1.1).
Different methods exist to take into account the altimetric consistency
of the triangulation [3] (Figures 3.5.1.2 and 3.5.1.3), but the altimetric
improvement is often performed to the detriment of the planimetric quality
of the triangulation. The choice of the points to insert is based in general
on a measure of importance, the simplest of these measures being the local
error on the considered point, that is to say the gap in Z between the TIN
and the raster model. It is a simple and fast measure [3] but one that
remains quite sensitive to the noise of the DEM and provides not very
meaningful results to the neighbourhood of altimetric discontinuities.
A more robust measure consists in evaluating the volume added by the
insertion of a point while taking the volume between the point to insert
and the triangle that is on its vertical. This measure will give some more
meaningful results in the case of light delocalizations on the sides of the
buildings (Figure 3.5.1.4).
At the time of the construction of a TIN by iterative insertion many
superfluous points are inserted. They are judged optimal to one given

226 Grégoire Maillet et al.
Figure 3.5.1.1 On the left the triangulation of a building and its perspective
representation with the criterion of Delaunay, on the right a
triangulation taking into account the altitudes.
Figure 3.5.1.2 At the time of the insertion of a point there is division of the
triangle into three. For each neighbouring quadrilateral the two
diagonals are tested. And the solution creating fewer errors in
Z is preserved.
instant and permit a convergence toward a good solution but become
redundant in the final result. The simplification of surface is therefore a
complementary and necessary approach for the construction of an optimal
TIN, that is to say describing in the best way the DEM with a minimum
of points. This simplification can be performed in a way similar to the
insertion: with a method of suppression of points in the triangulation and
a measure of the importance of points. But the simplification of TIN is a
problem very often met in image synthesis and thus specific methods have
been invented. The most frequent approach is not based on the suppression
of points, but on the contraction of a pair of points. That is to say

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Figure 3.5.1.3 For every triangle one looks for four characteristic points (one in
the triangle and one on each side). According to the result of this
research one applies one of the five possible divisions.
C
A
P
H
B
Figure 3.5.1.4 For a point P on a side of roof slightly delocalized the local error
PH is large whereas the volume of the ABCP tetrahedron is small.

228 Grégoire Maillet et al.
Figure 3.5.1.5 (a) urban DEM obtained by correlation; (b) transformation into
a TIN containing 5 per cent from initial points; (c) perspective
visualization of the TIN.
the replacement of a couple of points by a new point minimizing the
committed error [5].
References
[1] Haala N., Brenner C. Virtual city models from laser altimeter and 2D map
data. Photogrammetric Engineering and Remote Sensing, vol. 65, no. 7, July
1999, pp. 787–795.
[2] Maas H.-G., Vosselman G. Two algorithms for extraction building models from
raw laser altimetry data. ISPRS Journal of Photogrammetry and Remote
Sensing, vol. 54, nos. 2–3, July 1999, pp. 153–163.

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[3] Garland M., Heckbert P.S. Fast polygonal approximation of terrains and height
fields. Technical Report CMU-CS-95–181, Comp. Sci. Dept, Carnegie Mellon
University, September 1995, pp. 1–37.
http://www.cs.cmu.edu/~garland/scape
[4] Devillers O. Improved incremental randomized Delaunay triangulation. INRIA
Research Report no. 3298, November 1997, pp. 1–21.
[5] Garland M., Heckbert P.S. Surfig. Simplification using quadric error metrics.
SIGGRAPH 97 Proc., August 1997, pp. 209–216.
http://www.cs.cmu.edu/~garland/quadrics
3.5.2 Constitution of a DTM in the shape of a regular grid
of altitudes, from contour lines in vector mode
Patrick Julien
DSM reconstruction 229
3.5.2 Position of the problem. Notion of topographic surface
Suppose one is given a file containing a system of contour lines describing
the relief of a fixed geographical zone. To simplify, we call a contour line
what is in fact a section of a contour line, either closed, or stopped on
the edge of the zone. Every contour is assumed to be represented in vector
mode, i.e. described by vertices of a polygonal line, or by an ordered
sequence of points, say {pij (xij, yij, zj); i 1, . . ., n(j)} for the contour
1
M
l
2
1
p ij
2 c
N
1
p i+l, j
m cl
Figure 3.5.2.1 Contour lines in vector mode.
h
p n(j), j
h

230 Grégoire Maillet et al.
line placed to the rank j of the file; the coordinate z is the altitude, and
the x, y coordinates are relative to a cartographic representation. It is
important to point out that the contour line is not only the finite family
of points p ij, but the union of segments [p ij, p i1,j]; it is therefore a continuous
series, whose family p ij is one of the possible representations; in
particular, one is allowed to subdivide any segment [p ij , p i1,j ] into smaller
segments, which doesn’t change the shape of the curve. (See Figure 3.5.2.1.)
Now, one wishes to ‘interpolate’ in these contour lines a grid of points
with a grid interval h:
{m cl (x c, y l, z cl); c 1, . . ., N, l 1, . . ., M}, (3.22)
where x c ch, y l lh, regular in the x, y coordinates system. By ‘interpolating’,
we mean that every point must be situated on ‘the’ surface
represented by the contour lines, which surface is in principle well defined
by the rule of surveying these contours, according to which rule their plot
should be such that the user can always consider the slope between two
regular or intermediate curves as regular.
For example, the rule above means that if the user wants to draw a new
contour line situated at half height of two successive ones, he must place
it at an equal horizontal distance from the first ones, for if it were not the
case the slope would be steepest on one side of the new contour than on
the other, and therefore non-regular; more generally any intermediate
contour must be plotted between the two neighbouring contours, with
horizontal distances in ratio to vertical distances. In a more precise way,
we will interpret the rule while saying that, between two successive contours
and along a steepest slope line, the scalar value of the slope can be considered
constant. One so rejoins the rule according to which contour lines
must permit us to determine, with a sufficient precision, the elevations of
any ground point by simple linear interpolation.
We insist on the fact that it is necessary to admit that these rules give
place, for several users, to negligible interpretation differences, in other
words that contour lines suggest to all users the same ‘topographic’ surface
(simplified model of the real ground surface), obtained in practice by the
rule of the linear interpolation next along the line of steepest slope; it is
on this surface that the grid points m cl must lie.
So the interpolation of points m cl is transformed into the plotting of the
steepest slope lines, which are the orthogonal lines to contours (Figure
3.5.2.2). However, the tracing of these orthogonal lines, that essentially
consists in joining between each other bootjacks placed on curves, require,
as soon as orthogonal lines are a little wavy, a certain manual ability. One
guesses that the algorithmic transposition of this ability is delicate, and
the methods presented below only achieve it in an approximate way.
We are going to describe here methods of approximation by triangular

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irregular network surface, by thin plate spline surface, and by elastic grid
surface.
3.5.2.2 Approximation of the topographic surface by a
triangular irregular network surface (TIN surface)
DSM reconstruction 231
Figure 3.5.2.2 Handmade drawing of the steepest slope lines, orthogonal to
contours.
Definitions relative to triangulations
Let’s first specify the vocabulary used. A triangulation of a domain D of
the plane is a finite family of triangles of which union is D, of non-null
areas, of which any two have in common either nothing, or a vertex, or
a side. A triangulation is called Delaunay’s if the open circle (i.e. a circle
without its edge) circumscribed to any triangle contains no other triangle
vertex. One shows that, given a finite family {mi} of points of the plane,
there exists a triangulation of Delaunay, and algorithms to construct it,
whose vertices of triangles are exactly the points mi; the triangulation is
unique if there are never four cocyclic points mi, mj, mh, mk. A triangulated
surface is a connex surface, union of a family of (plane) triangles of
the space, of non-null areas, of which any two have in common either
nothing, or a vertex, or a side.

232 Grégoire Maillet et al.
Conditions to be observed by a TIN surface approximating the
topographic surface
We have now to approximate the topographic surface with a triangulated
surface fitted on contour lines. The searched-for surface here is with
irregular faces, and the horizontal positions of triangle vertices are not a
priori known; this problem is therefore distinct from fitting a surface whose
horizontal positions of vertices would form a fixed in advance network,
a problem in which only the altitudes of triangle vertices are unknown.
It seems natural that triangles’ vertices are points taken on contour lines,
because there doesn’t appear a simple way to define other points for this
use. Besides, every triangle must be an acceptable approximation of the
topographic surface, which requires that its three sides are close to this
surface. That in particular notably forbids that a triangle edge ‘crosses’ a
contour (in the sense that their horizontal projections intersect each other),
because, in general, such an edge no longer lies on the topographic surface;
for example, on Figure 3.5.2.3, the AB side crossing the contour (z + e)
does not lie on the topographic surface whose profile is AIB. In particular,
a triangle cannot have its vertices on three contours of different
altitudes, otherwise one of its sides would ‘cross’ a contour (ABC triangle).
A triangle must not have its three vertices on the same curve, otherwise
it would be horizontal and would not lie on the topographic surface (DEF
triangle). It is therefore necessary that every triangle has its vertices on
two consecutive contours; in addition, the side defined by the two vertices
placed on the same contour must be confounded with the contour (GHJ
triangle) for, if it were not the case, this side could not lie on the surface.
z
E
z+e
D
H
F
z+2e
J
C
G
B
I
Figure 3.5.2.3 ABC is an unauthorized triangle because it touches three contours;
DEF is unauthorized because it touches only one contour; GHJ is
an authorized triangle, touching two consecutive contours, with
one side along a contour.
A

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It is necessary to also observe, for example on the GHJ triangle, that
the smaller the HJ side in relation to the sides GH and GJ, the better is
the approximation of the topographic surface; it is therefore a priori preferable
that sides bordering the curves be short.
It is finally necessary that triangles overlap the whole zone described by
contour lines, so that every point of any contour line is on a side of a
triangle; and that above every horizontal position (x, y) there is only one
triangle. In these conditions, the horizontal projections of triangles constitute
a plane triangulation. Once the future triangle vertices (X i, Y i, Z i) are
chosen, one will therefore get a triangulated surface by constructing a
plane triangulation whose vertices of triangles are points (X i, Y i).
Construction of a triangulated surface
Among all possible plane triangulations, that of Delaunay seems a reasonable
choice, because its geometric properties are known, unlike a
triangulation that would be constructed with the help of heuristics.
It remains to choose the points devoted to be the triangles’ vertices. It
is necessary to take at least all points pi,j initially defining the contour
lines (except possibly those aligned with their predecessor pi1,j and their
successor pi1,j , which doesn’t modify the tracing of the contour). However,
if the distance between two consecutive points pi,j, pi1,j is large in relation
to their horizontal distances d1, d2 to neighbouring curves, the triangulation
of Delaunay risks the construction of triangles crossing a curve,
therefore forbidden.
For example from the four points p, p′, q, r of Figures 3.5.2.4(a) and
(b), one can construct either the authorized pair of triangles {pp′q, pp′r},
or the pair {pqr, p′qr}, forbidden because the side pq ‘crosses’ a contour.
In the case where angle (q) angle (r) < < angle (p) angle (p′) (Figure
3.5.2.4(a)), the pair of triangles is compatible with the condition of
Delaunay because neither r is in the pp′q circle, nor q in the pp′r circle,
whereas the {pqr, p′qr} pair is incompatible since p is in the p′qr circle
and p′ in the pqr circle. In the opposite case where angle (p) angle (p′)
< < angle (q) angle (r) (Figure 3.5.2.4(b)), the pair {pqr, p′qr} is Delaunay
compatible, but not the pair {pp′q, pp′r}.
So in order that the Delaunay triangulation constructs the acceptable pair,
it is necessary to be in the case: angle (q) angle (r) < ; as angle (q) < 2
Arctan (d/2d1 ) and angle (r) < 2 Arctan (d/2d2 ), it is sufficient that:
Arctan d
2d 1 Arctan d
2d <
2 2 Arctan d
2d 1 Arctan 2d1 d ,
i.e. d < 2 √d 1 d 2 .
DSM reconstruction 233
(3.23)

234 Grégoire Maillet et al.
d 1
d 2
p
q q
r
d
p′
Figure 3.5.2.4 (a) (left) Topographically authorized pp′q and pp′r triangles are
selected by Delaunay triangulation; (right) Topographically
unauthorized triangles pqr and p′qr are rejected by Delaunay
triangulation.
d 1
d 2
p
q
r
p′
d d
Figure 3.5.2.4 (b) (left) Triangles pq′q and pp′r are topographically authorized,
but rejected by Delaunay triangulation; (right) Triangles pqr and
p′qr are topographically unauthorized, but selected by Delaunay
triangulation.
If d does not verify this condition, additional points between p and p′ are
necessary, at mutual distances d′

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p
p′
p′′
q
DSM reconstruction 235
Figure 3.5.2.5 Topographically authorized triangle pp′q is rejected by Delaunay
triangulation; instead the horizontal unauthorized triangle pp′p′′ is
selected.
r
q m
q 3
q2
q 1
q
Figure 3.5.2.6 From the horizontal triangles (in grey) selected by Delaunay
triangulation, a polygonal line qq 1 q 2 ... q m is defined, with each
q i in the middle of an edge, and: Altitude (q) > altitude (q 1 )>
altitude (q 2)>...>altitude (q m) > altitude (r).
One constructs then a new Delaunay triangulation (Figure 3.5.2.7), if
necessary by adding some intermediate points on segments [q 1, q 2],
[q 2, q 3], . . ., [q m1, q m], to guarantee that no triangle rides the line qr. Then
the TIN surface thus constructed is a relatively satisfactory approximation
of the topographic surface.
Going from TIN surfaces to the regular grid of altitudes
Once the surface with triangular faces is obtained, it remains to determine
in which triangle of the triangulation each mcl point is projected, to form

236 Grégoire Maillet et al.
Figure 3.5.2.7 A part of the improved Delaunay triangulation (including the
additional vertices q q 1 q 2 ... q m) with topographically authorized
triangles.
the equation z ax by d of the plane of this triangle, and to calculate
the elevation z cl ax c by l d.
3.5.2.3 Approximation of the topographic surface by a thin
plate spline surface
Definition
Thin plate spline surfaces answer the following problem of interpolation:
given a sample of n points of the plane mi (xi, yi) and their elevation
zi, find a function Z(x, y) so that Z(xi, yi) zi for i 1, . . ., n and that
the integral
K(Z) RR
(3.24)
be minimal; Z′′
xx , Z′′
xy , Z′′
yy designate partial second derivatives.
Thin plate splines also answer the adjustment problem: besides, given n
weight values i > 0, find a function Z(x, y) such that the quantity:
E(Z) K(Z) n
Z′′
xx(x, y) 2 2Z′′
xy(x, y) 2 Z′′
yy(x, y) 2 dx dy
i1
i Z(x i, y i) z i 2
(3.25)
be minimal.
J. Duchon showed (1976) that each of these problems admits a solution
and only one (under the condition – always true – that the sample
counts at least three non-aligned points). He also characterized solutions
as functions in the shape:

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with
where
(3.26)
Note that Z(x, y) is defined by continuity at (x i, y i) points since (r) tends
toward 0 when r tends toward 0.
More precisely, the solution of the interpolation problem is the function
Z(x, y) of the shape Eqn (3.26) such that Z(x j, y j) Z j(j 1 . . . n); i.e.
whose n3 coefficients a 1, . . ., a n,b 0, b 1, b 2 verify the n3 equations:
with
(3.27)
The solution of the adjustment problem weighted by the family { i }
is the function Z (x, y) of shape (3.26) such that (8a j/ j) Z (x j, y j)
z j (j 1 . . . n), i.e. whose n3 coefficients verify the n3 equations:
with
Z(x, y) i
i
i
i
8aj
i
j
a i 0, i
a i 0, i
i
a i 0, i
a ir i (x, y) b 0 b 1 x b 2 y ,
a i x i 0, i
r i(x, y) √(x x i) 2 (y y i) 2 , (r) r 2 ln r.
a i r i (x j , y j ) b 0 b 1 x j b 2 y j z j ( j 1,… , n),
a i x i 0, i
ai ri (xj , yj ) b0 b1xj b2yj zj (j 1, … , n), (3.28)
a i x i 0, i
a i y i 0,
a i y i 0.
a i y i 0.
DSM reconstruction 237
Moreover, these equations clearly show the interpolation problem as the
limit of the adjustment problem when weights j become arbitrarily large.
A surface Z(x, y) of the shape (3.26) has been called a thin plate spline
by reason of the physical interpretation of the integral K(Z), roughly proportional
to the energy of bending of a thin plate of equation z Z(x, y).
Geometric significance of the integral K(Z)
Geometrically, the integral K(Z) represents the ‘global’ curvature of the
surface Z(x, y). Indeed a Z function, supposed twice differentiable at

238 Grégoire Maillet et al.
(x, y), is approximated at the points (xr, ys) near (x, y) by its Taylor
polynomial of degree 2:
Z(xr, ys) Px,y(r, s) (3.29)
where Px,y (r, s) Z(x, y) Z′ xr Z′ ys is the tangent plane in (x, y).
One sees that the surface is all the more distant from its tangent plane
(and so all the more concave), as Z′′ xx, Z′′ xy Z′′ yx, Z′′ yy are more distant
2 2 2 2 2 from 0, or as Z′′ xx , Z′′ xy , Z′′ yy are larger; so the quantity Z′′ xx 2Z′′ xy
2 Z′′ yy measures the curvature of the Z surface in every point.
1
2 Z′′ xxr 2 Z′′ xyrs Z′′ yxrs Z′′ yys2, REMARK
2 2 2 The quantity Z′′ xx 2Z′′ xy Z′′ yy has the advantage over similar measures
such as |Z′′ xx| |Z′′ xy| |Z′′ yy| or sup(|Z′′ xx|, |Z′′ xy|, |Z′′ yy|) of being a characteristic
of the surface, invariant by a rotation of the orthonormal reference
frame, i.e. by change of variable (x, y) (X cos a Y sin a, X sin a Y
cos a). For the U parametrization of the Z surface defined by U(X, Y)
Z(X cos a Y sin a, X sin a Y cos a) Z(x, y), one has:
U′′ XX(X,Y)
Z′′
xx(x, y) cos 2 a 2Z′′
xy(x, y) sin a cos a Z′′
yy(x, y) sin 2 a
U′′ XY (X,Y)
U′′ YY(X,Y)
Z′′
xx(x, y) sin 2 a 2Z′′
xy(x, y) sin a cos a Z′′
yy(x, y) cos 2 a.
Writing: sin 2A 2Z′′
xy /C, cos 2A (Z′′
xx Z′′
yy )/C, where
C √(Z′′ xx Z′′ yy) 2 2 4Z′′ xy ,
one gets the expressions:
U′′ XX (Z′′ xx Z′′ yy)
2
C
cos 2(a A)
2
U′′ XY C
sin 2(a A)
2
Z′′
xx (x, y) sin a cos a Z′′
xy (x, y) (cos 2 a sin 2 a)
Z′′
yy (x, y) sin a cos a
U′′ YY (Z′′ xx Z′′ yy )
2
C
cos 2(a A)
2
(3.30)
(3.31)

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from which it is easy to verify that
U′′ XX 2 2U′′XY 2 U′′
YY 2 Z′′
xx 2 2Z′′
xy 2 Z′′
yy 2 .
Justification of the approximation of the topographic surface by
a thin plate spline surface
One understands now that the condition of minimality of the integral K(Z)
means that between sample points the ‘global’ curvature of the surface is
as weak as possible, or else that variations of the tangent plane, and therefore
of the slope, are as weak as possible. So a thin plate spline surface
adjusted on contour lines presents a slope as regular as possible between
contour lines, which is compatible with the definition of the topographic
surface.
We should add that the maximal regularity of the thin plate spline
surface applies at a time in all directions, and in particular in the horizontal
direction, which notably has the effect of ‘straightening’ the surface
exaggeratedly on crests and in thalwegs; the adjusted surface may therefore
present artefacts, and then describes the topographic surface only
roughly.
Implementing the approximation by a thin plate spline surface
STEP 1. CONSTITUTION OF AN APPROPRIATE SAMPLE OF POINTS
To use the method, it is necessary to first select on contour lines a sample
of points, while remembering that a segment of curve [p ij , p ii, j ] must
influence the surface by all its points, and not only by its extremities. By
taking as a sample only the initially given points p ij, one sees that all
segments would have the same influence, whereas it seems natural that a
segment influences according to its length. Therefore one should cut all
contours into small elementary ‘segments’ of similar length, in order to
assure an influence proportional to the length.
STEP 2. CHOICE OF WEIGHTS IN THE CASE OF THE THIN PLATE SPLINE
SURFACE OF ADJUSTMENT
A thin plate spline surface of adjustment Z(x, y) by definition minimizes
the quantity:
E(Z) K(Z) i
preferably written
i Z(x i , y i ) z i 2 ,
DSM reconstruction 239

240 Grégoire Maillet et al.
where
r i is the relative weight of the point (x i , y i , z i ) and the P weight fixes the
importance of the adjustment criterion
in relation to the curvature criterion K(Z).
It is then necessary to choose the weight P and weights r i .
(a) Let us first examine the effect of the weight P.
To P > 0, corresponds a unique thin plate spline surface, denoted Z P ,
minimizing E P (Z) K(Z) Pe(Z); in the same way, to Q > 0 corresponds
the surface Z Q , minimizing E Q (Z) K(Z) Qe(Z).
Because of the minimal character of E P (Z P ) and of E Q (Z Q ), one has
Or else:
E P (Z) K(Z) P i
P i
e(Z) i
i and r i i
r i Z(x i, y i) z i 2
E P(Z P) E P(Z Q) and E Q(Z Q) E Q(Z P).
K(Z P) Pe(Z P) K(Z Q) Pe(Z Q),
K(Z Q ) Qe(Z Q ) K(Z P ) Qe(Z P ).
Adding on the one hand the inequalities,
K(Z P) Pe(Z P) K(Z Q) Pe(Z Q).
K(Z P ) Qe(Z P ) K(Z Q ) Qe(Z Q ),
and on the other hand the inequalities,
QK(Z Q) PQe(Z Q) QK(Z P) PQe(Z P),
PK(Z Q) PQe(Z Q) PK(Z P) PQe(Z P),
one gets the inequalities,
P ;
(P Q)e(Z P) (P Q)e(Z Q)
r i Z(x i , y i ) z i 2 ,

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and
(P Q)K(Z Q ) (P Q)K(Z P ), (3.32)
showing that if P>Q, then K(Z P ) K(Z Q ) and e(Z P ) e(Z Q ); it means
that the surface Z Q is less bent than Z P , or ‘smoother’, but not so well
adjusted to the sample. In particular the interpolation thin plate spline Z ,
limit of Z P when P becomes arbitrarily large, is perfectly adjusted to the
sample, but is less smooth than any thin plate spline of adjustment Z Q.
(b) We suppose the P weight henceforth fixed, and we consider the weights
r i .
The simplest choice is of course to give the same weight r i 1/n to all
points.
This choice is not satisfactory because the distribution of points(x i, y i)
can be heterogeneous because of the irregular horizontal distribution of
contours, and of variations of the sampling interval along contours.
Uniform weights would make the adjustment surface Z(x, y) deflect toward
portions of land finely sampled, which is unacceptable because Z has no
reason to be affected by the sampling interval.
To avoid this inconvenience, it is therefore necessary that weights r i are
small where the sample is dense, and larger where the sample is sparse.
In other words a weight r i must be weak when the point (x i, y i) is representative
of a small area A i, and large when the point is representative of
a large one, which brings about that r i is an increasing function f(|A i|) of
the area |A i|. Besides, this function can only be linear, because if one unifies
two contiguous parcels, A i, A j in one A i ∪ A j, then the weight f (|A i ∪ A j|)
f(|A i| |A j|) of the union must be the sum of weights:
f(|A i | |A j |) r i r j f(|A i |) f(|A j |). (3.33)
Thus, ri k|Ai|, and the condition imposes
ri 1
k
1
A i .
DSM reconstruction 241
It remains to specify what is a parcel A i represented by the point
(x i , y i , z i ); it is natural to define it as the set of points (x, y) that are closer
to (x i, y i) than to the other (x j, y j) points; one knows that this set is a
polygon V i and that the family {V i; i 1, . . ., n} forms the Voronoï diagram
associated with points (x i,y i).
Finally, a coherent system of weight can be defined by:

242 Grégoire Maillet et al.
r i
where |V i | designates the area of the Voronoï polygon V i .
STEP 3. RESOLUTION OF THE LINEAR SYSTEM
(3.34)
The following step consists in solving the linear system of n3 equations
giving coefficients a 1 , . . ., a n , b 0 , b 1 , b 2 .
Denoting c ij r i (x j , y j ) 2 ln r i (x j , y j ) this system becomes in matrix form:
⎧
⎪
⎪
⎪
⎪
⎩
j
8/ 1
c 12
…
c 1n
1
x 1
y 1
which can be written as
C F
T
F 0 a
b Z
0
Note that,
V i
. (3.35)
ri(xj, yj) √(xj xi) ,
2 (yj yi) 2 rj(xi, yi) therefore c ji c ij; the matrix C is therefore symmetrical.
Note that neither the matrix
C F
T
F 0
V j ,
c 21
8/ 2
…
c2n 1
x2 y2 …
…
…
…
…
…
…
nor its opposite, are positive; for example, if a = (1, 0, 0, …, 0) and b =
(b 0 , 0, 0), one gets:
(aT bT ) C F
T
F 0 a
b
c n1
c n2
…
8/ n
1
xn yn 8
2b0 1
1
1
…
1
0
0
0
x 1
x 2
…
x n
0
0
0
which can be 0 or 0 according to the value of b 0 .
C. Carasso in Baranger (1991) suggests solving the system (3.35) as
follows. One factorizes F as F QR where Q is an (n, n) orthogonal
matrix, and R an (n, 3) matrix in the shape
y1 y2 …
y n
0
0
0
⎫
⎪
⎪
⎪
⎪
⎭
⎧
⎪
⎪
⎪
⎪
⎩
a 1
a 2
…
a n
b 0
b 1
b 2
⎫
⎪
⎪
⎪
⎪
⎭
⎧
⎪
⎪
⎪
⎪
⎩
z1 z2 …
z n
0
0
0
⎫
⎪
⎪
⎪
⎪
⎭

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R U
0
,
with U a (3, 3) triangular superior matrix. F is of rank 3, since there are
at least three non-aligned points, therefore R is of rank 3, and thus U is
invertible. So, one can write (here I is the (3, 3) identity matrix):
C F
T
F 0 Q
0 0
I QTCQ T
R
R
0
so that the system (3.35) is equivalent to the system
0
(3.36)
(3.37)
Writing by blocks, Q (Q 1 Q 2 ), Q 1 (n, 3) matrix, Q 2 (n, n3) matrix, and
this system is written:
Q1 TCQ1 T
Q2CQ1 U T
T Q1CQ2 T
Q2CQ2 0
0 QT
QTCQ R
T R 0 d
b QTZ 0 , a Qd .
d d 1
d 2 , d 1(3) vector, d 2(n3) vector,
U
0
0 d1 d2 b Q1 TZ (3.38)
one deduces U T d 1 0, thus d 1 0; from the equation Q 2 T CQ2d 2 Q 2 T Z,
one deduces d 2 , from where a Q 2 d 2 ; from the equation Q 1 T CQ2 d 2 Ub
Q 1 T Z, or Ub Q1 T (Z Ca), one finally extracts b.
It is necessary to notice that the C matrix is full, therefore the matrix
Q 2 T CQ2 also; one will see that to the contrary the ‘elastic’ grid method
drives to a sparse system, allowing larger size systems to be processed with
the same memory resources.
STEP 4. CONSTITUTION OF THE REGULAR GRID
T
Q2Z 0 , a Q1d1 Q2d2 ;
This immediate step consists in calculating, by the formula (3.26), the altitudes
z cl Z(x c , y l ) at the grid nodes.
3.5.2.4 Approximation of the topographic surface by an elastic
grid surface (de Masson d’Autume, 1978)
Definition
An elastic grid surface can be introduced as a discrete approximation of
a thin plate spline surface of adjustment Z(x, y), defined in §3.5.2.3; one
knows that Z(x, y) minimizes a quantity:
I
DSM reconstruction 243

244 Grégoire Maillet et al.
E(Z) K(Z) i
(3.39)
As our final objective is not the Z(x, y) surface, but only the set of its
values zcl Z(xc, yl) at the nodes of a regular grid {xc ch; c 1, . . ., N}
× {yl lh; l 1, . . ., M}, one can try to set a problem whose unknown is the
set {zcl } directly. Thus we shall replace the E(Z) quantity by an approached
quantity that is a function of the zcl only.
(1) On the one hand one has to replace the integral
One first approaches it by Riemann sum:
K(Z) h 2 c,l
where c 1:N, l 1:M.
i Z(x i , y i ) z i 2 .
K(Z) Z′′
xx 2 2Z′′
xy 2 Z′′yy 2 dxdy.
Z′′
xx (x c , y l ) 2 2Z′′
xy (x c , y l ) 2 Z′′
yy (x c , y l ) 2 ,
(3.40)
One can then write the following eight Taylor formulae at point (x c, y l):
zc1,l zcl Z′ xh Z′′ xx h2
Z′′′ xxx
2 h3
6 o(h3 )
zc1,l zcl Z′ xh Z′′ xx h2
Z′′′ xxx
2 h3
6 o(h3 )
zc,l1 zcl Z′ yh Z′′ yy h2
Z′′′ yyy
2 h3
6 o(h3 )
zc,l1 zcl Z′ yh Z′′ yy h2
Z′′′ yyy
2 h3
6 o(h3 )
zc1,l1 zcl Z′ xh Z′ yh (Z′′ xx 2Z′′ xy Z′′ yy) h2
2
h3
(Z′′′ xxx 3Z′′′ xxy 3Z′′′ xyy Z′′′ yyy )
6 o(h3 )
zc1,l1 zcl Z′ xh Z′ yh (Z′′ xx 2Z′′ xy Z′′ yy) h2
2
(Z′′′ xxx 3Z′′′ xxy 3Z′′′ xyy Z′′′ yyy) h3
6 o(h3 )
zc1,l1 zcl Z′ xh Z′ yh (Z′′ xx 2Z′′ xy Z′′ yy ) h2
2

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zc1,l1 zcl Z′ xh Z′ yh (Z′′ xx 2Z′′ xy Z′′ yy ) h2
2
h3
(Z′′′ xxx 3Z′′′ xxy 3Z′′′ xyy Z′′′ yyy ) (3.41)
6
adding the first and second formulae, then the third and fourth, and finally
the last four, one deduces:
o(h3 );
Z′′
xx (x c , y l ) (z c1,l 2z cl z c1,l)
h 2 o(h)
Z′′
yy (x c , y l ) (z c,l1 2z cl z c,l1)
h 2 o(h)
(3.42)
These values permit us to approximate the integral K(Z) by the quantity
function of the vector z {zcl} of RMN Z′′ xy (xc , yl )
:
(zc1,l1 zc1,l1 zc1,l1 zc1,l1) 4h 2 o(h).
K h(z)
1
h 2 N1
c2
N1
c2
(2) On the other hand one has to replace in
e(Z) i
M1
(zc1,l1 zc1,l1 zc1,l1 zc1,l1) l2
2 /8 .
(3.43)
every Z(x i , y i ) by a function of the vector z.
One will adopt a representation by a piecewise bilinear or bicubic function
Z(x, y) c,l
M
(zc1,j 2zcl zc1,l) l1
2 N
c1
i Z(x i, y i) z i 2
zcl V x
h c V y
l h
with, in the bilinear case, V(t) Q(t) sup(1 |t |, 0) and in the bicubic
case:
3
2 t
V(t) U(t) 3 5
2 t 2 1
1
2 t 3 5
2 t 2 4t 2
0
DSM reconstruction 245
(Z′′′ xxx 3Z′′′ xxy 3Z′′′ xyy Z′′′ yyy) h3
6 o(h3 )
M1
(zc,l1 2zcl zc,l1) l2
2
if t 1
if 1 t 2
if t 2
(3.44)

246 Grégoire Maillet et al.
e(Z) is then replaced by
e h(Z) i
Finally the E(Z) quantity is replaced by the quantity function of
One defines the elastic grid surface associated with the sample {(x i, y i, z i);
i 1, . . ., n} as the surface
Z(x, y) c,l
defined by the vector z {z cl } that minimizes the quantity E h (z).
Existence and unicity of the solution for the minimization
problem of Eh(z) The quantity Eh(z) is a quadratic function of z {zcl}, which therefore can
be minimized explicitly.
In a precise way, one introduces the vectors Ccl ,Dcl ,Fcl ,Bi such as
c,l
for example,
C T cl
= (0 … 0 1 –2 1 0 … 0) .
One then sees that:
e h(z) i
i c,l
z {z cl}, E h(z) K h(z) e h(z).
T zc1,l 2zcl zc1,l Ccl z
T zc,l1 2zcl zc,l1 Dcl z
K h(z) 1
h 2 cl
z T i
z cl V x i
h c V y i
h l z i 2
.
zcl V x
h c V y
l h
z c1,l1 z c1,l1 z c1,l1 z c1,l1 F cl T z
zcl V xi h c V yi h l BT i z ,
c1,l cl c1,l
zT T CclCcl z cl i (z T B i z i) (B i T z zi)
i B i B i T z 2 i
zT T 1
DclDcl z
8 cl i z i B i T
z i
zT T FclFcl z
i z i 2 ,
(3.45)
(3.46)

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so that, putting:
A 1
h 2 cl
b i
one can write E h (z) as:
The matrix A is symmetrical. It is positive because
(3.47)
whatever the value of z.
One intends to show that the matrix A is positive definite, which means
that z T Az can be 0 only if z 0; this property will guarantee the existence
and the unicity of the solution of the problem.
Let us suppose therefore that z T Az for a certain z.
Then C T cl z 0 for any c, l, which implies z cl z 1l (c 1)(z 2l z 1l)
In the same way D T cl z 0 for any c, l, which implies z cl z c1 (l 1)
(z c2 z c1).
One deduces then:
zcl z11 (c1)(z21 z11) (l1)(z12 z11)
(c1)(l1)(z22 z12 z21 z11 )
a0 a1c a2l a3cl (3.48)
for any c, l;
from where
T CclCcl cl i z i B i c i
E h (z) z T Az 2b T z c.
zTAz 1
h2 T 2 (Ccl z) cl
cl
i
i (B i T z) 2 0
T 1
DclDcl
8 cl i z i 2
T 2 1
(Dcl z)
8 cl F T
cl z z c1,l1 z c1,l1 z c1,l1 z c1,l1 4a 3 .
The hypothesis z T Az 0 also implies F T cl z for any c, l, from where a 3 0.
Finally: z cl a 0 a 1c a 2l for any c, l.
DSM reconstruction 247
F T clFcl i T (Fcl z) 2
iB iB i T

248 Grégoire Maillet et al.
One has then:
B i T z
However, one can show that the V function, when it designates the Q
linear interpolation function as well as the U cubic interpolation function,
verifies the identities:
c
cl
from where:
a 0 c
But the hypothesis z T Az 0 implies B i T z a0 a 1(x i/h) a 2(y i/h) 0
for any i; now one can suppose that the sample counts at least three (x j,
y j), (x k, y k), (x p, y p) non-aligned points; these three points verify the system
a xj 0 a1 a 1 c
a 2 c
V(x c) 1 and c
B i T z a0 a 1 x i
h a 2 y i
h .
y j
h a2 0,
h
cV x i
h c l
V x i
h c l
of non-null determinant (x p – x j )(y k – y j ) – (x k – x j )(y p – y j ), which is
possible only if a 0 a 1 a 2 0. Therefore z 0; one has thus shown
that A is positive definite.
A is then invertible, and one can write therefore:
E h (z) (z A 1 b) T A(z A 1 b) c b T A 1 b c b T A 1 b,
which shows that E h(z) reaches its minimum cb T A 1 b if and only if z
A 1 b. In other words the problem of minimization of E h(z) admits a solution
z and only one given by the equation Az b.
Structure of the A matrix
One has: A A1 A2 where
(a0 a1c a2l) V xi h c V yi l h
V x i
h c l
V yi l h
V yi l h
lV yi l .
h
cV(x c) x for any x;
xk a0 a1 h a yk 2 0,
h
xp a0 a1 h a yp 2 0 h

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A 1 1
h 2 cl
A, A 1, A 2 are (MN, MN) matrixes (M: number of lines, N: number of
columns of the grid).
If we expand A, we get:
A 1 1
h 2
where I is the (N, N) identity matrix, X and Y are (N, N) matrixes:
X
Y
Expanding A 2 in the case of bilinear model one gets:
A 2
⎧
⎪
⎪
⎪
⎪
⎩
⎧
⎪
⎪
⎪
⎪
⎩
⎧
⎪
⎩
1
2
1
1
0
1
⎧
⎪
⎪
⎩
IX Y
8
X
X
2I
I Y
8
2
5
4
…
0
1
0
…
X
X
…
C cl C T cl cl
1
4
6
…
1
1
0
2
…
1
X
…
X
2I
5IX Y
8
4I
…
1
0
…
0
1
…
X
X
1
4
…
4
1
1
…
2
0
1
X
X
D cl D T cl 1
8 cl
1
…
6
4
1
⎫
⎪
⎪
⎭
I Y
8
4I
6IX Y
4
…
I Y
8
…
4
5
2
…
0
1
0
1
0
1
I Y
8
4I
…
…
I Y
8
1
2
1
⎫
⎪
⎪
⎪
⎪
⎭
⎫
⎪
⎪ .
⎪
⎪
⎭
DSM reconstruction 249
F cl F T cl ,
I Y
8
…
6IX Y
4
4I
I Y
8
A 2 i
…
4I
5IX Y
8
2I
i B i B i T
…
I Y
8
2I
IX Y
8
,
⎫
⎪
⎭

250 Grégoire Maillet et al.
where each X is a matrix of the shape
X
⎧
⎪
⎪
⎩
•
•
A 1 and A 2 are written in the shape of (M, M) matrixes of (N, N) size
blocks.
Every line of the matrix A includes a maximum of 21 non-null coefficients
on a total of MN; for a grid M 100, N 100, there are therefore
more than 99.79 per cent of zero coefficients. One sees that A is really a
sparse matrix, as stated.
References
•
•
…
•
…
•
…
•
•
•
•
⎫
⎪
⎪
⎭
Carasso C. (1991) Lissage des données à l’aide de fonctions spline, in J. Baranger
(ed.) Analyse numérique, Hermann, pp. 357–414.
de Masson d’Autume G. (1978) Construction du modèle numérique d’une surface
par approximations successives. Application aux modèles numériques de terrain
(M.N.T.), Bulletin de la Société française de photogrammétrie et de télédétection,
no. 71–72, pp. 33–41.
de Masson d’Autume G. (1979) Surface modelling by means of an elastic grid,
Photogrammetria, no. 35, pp. 65–74.
Duchon J. (1976) Interpolation des fonctions de deux variables suivant le principe
de la flexion des plaques minces, Revue Française d’Automatique, Informatique
et Recherche Opérationnelle (R.A.I.R.O.) Analyse numérique, vol. 10, no. 12,
décembre, pp. 5–12.
3.5.3 Merging contour lines and 3D measurements from
images
Nicolas Paparoditis
The two techniques that have been described in the previous paragraphs,
for understandable pedagogic and clarity reasons, have been developed
separately. Nevertheless, the DSM reconstruction from contour lines can
be improved by adding 3D points processed by photogrammetric means to
solve ambiguities between all possible triangulation of contour lines. In the
same way, contour lines can be injected as constraint lines in the process
of triangulation of all 3D points that can processed from the images. Both
techniques lead to a constrained triangulation. Nevertheless, these merging
processes will have the chance of succeeding if both 3D information are
homogeneous in accuracy and precision and definitely describe the same
surface.

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3.5.4 Generating a DTM with sparse 3D points and
characteristic features
Nicolas Paparoditis
DSM reconstruction 251
A DTM can be generated manually by plotting well-chosen sparse on
ground 3D points in a stereo display. The spatial localization of these
points is determined by the operator and their elevation can be also manually
plotted or automatically generated through the stereo matching
methods we have discussed earlier. The spatial density of the points depends
on the local roughness of the landscape and on the desired DTM quality.
A TIN-like surface can be generated from these points with a 2D Delaunay
triangulation, as shown in Figure 3.5.4.1 (a) and (b).
Instead of plotting much denser points (increasing production times)
around terrain break lines to render locally the relief morphology, the
operator can plot the break lines themselves and use these lines to constrain
locally the triangulation. In practice, we destroy all triangles overlapping
x
y
(a) (b)
f g
j
k a
i
b h
l
c
m
n
d a
e
o
p
(c) (d)
Figure 3.5.4.1 (a) in black sparse cloud of 3D points and in grey the slope beak
line; (b) 2D triangulation of all points in the cloud; (c) all triangles
overlapping the break line are removed and (d) the remaining
space is triangulated under the constraint that the new triangles lie
on the break line segments.

Figure 3.5.4.2 (a) Triangulation without characteristic constraint lines.
Figure 3.5.4.2 (b) Triangulation with characteristic constraint lines.

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Extraction of characteristic lines of the relief 253
the break line and we triangulate the remaining space. For instance, in the
case of an open slope break line as shown on Figure 3.5.4.1, the triangulation
of this empty space can be seen as the triangulation of the polygon
(c, f, g, h, k, l, m, n, o, p, f, c, d, e, d, c, b, a, b, c) in the Figure
3.5.4.1 (c) example, where c f is the smallest segment joining the break
line points and the surrounding triangle points.
Figures 3.5.4.2 (a) and (b) show some triangulation results on a real set
of data (points and characteristic terrain line) plotted on a digital photogrammetric
workstation.
3.6 EXTRACTION OF CHARACTERISTIC LINES OF THE
RELIEF
Alain Dupéret, Olivier Jamet
3.6.1 Some definitions bound to the relief
3.6.1.1 Preliminary definitions
The building of the relief results from many endogenous actions and exogenous
phenomena such as lithology, climatic variations, vegetation,
anthropic activities. . . . The hydrographic network is a set of particularly
useful morphological objects to characterize the relief. The description of
this last by the characteristic elements leans on a mathematical representation
that depends on:
• the type of data capture: the surface itself, the cartographic representation;
• the mode of acquisition: direct surveys, digitization, photogrammetric
restitution;
• the mode of altitudes distribution: contour line, regular or irregular
set of points.
In practice, it is desirable to do a separation between aspects bound to
the acquisition of the ground characteristic elements and those bound
to the mathematical representation of the surface. Otherwise, notions of
thalwegs and rivers are often assimilated, and this leads to confusions
such as how to assimilate the relief and the process of water streaming,
even if they are the most often linked; the superficial outflow most often
takes place in the sense of the local or regional line of stronger slope, but
the geology (by the presence of hard or soft rock) and the fracturation
can also intervene.
First, a simple topological mathematical presentation will be given for
the main remarkable elements of the relief. Then, several operative modes
will be presented on the basis of some important studies.

254 Alain Dupéret and Olivier Jamet
3.6.1.2 Definitions of the main characteristic elements of the
relief
The definitions that follow are based upon a quite simplistic modelization
of the reality: we will suppose that the topographic surface is correctly
described by a function z H(x, y), continuous and twice derivable.
Obviously it is only an approximation, as the topography presents many
similarities with fractal structures, and presents discontinuities at every
scale of observation. Nevertheless, this approach allows for much simpler
definitions of the characteristic elements of the relief.
The main remarkable points
THE SUMMIT
The summit is the high point isolated representative of the local maximum
of the H function. In practice, one generally uses the following (incomplete)
characterization:
THE BASIN
The basin is the low point isolated representing the local minimum of the
H function. In practice:
which means therefore that radii of curvatures in the principle planes are
negative.
THE PASS
(X 0 , Y 0 ) is a summit if H′ x(X 0, Y 0) 0
H′ y (X 0 , Y 0 ) 0
H′′
xx(X 0, Y 0) < 0 and H′′
yy (X 0, Y 0) < 0
(X0 , Y0 ) is a basin if H′ x(X0, Y0) 0
H′ y (X0 , Y0 ) 0
,
H′′ xx(X0, Y0) > 0 and H′′ yy (X0, Y0) > 0
The pass is an origin point of at least two divergent water streams. The
notion of pass evokes a point as much as a surface. From the macroscopic
point of view, it is a region in which two divergent valleys separating two
summits meet that is, mathematically, a saddle point. In practice:
(X0, Y0) is a pass if H′ x (X0 , Y0 ) 0
H′ y (X0, Y0) 0
H′′
xx(X 0, Y 0) · H′′
yy (X 0, Y 0) < 0
.

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This situation implies the existence of such a point, that any infinitesimal
circle around it shows at least a double slope alternance. The water stream
may, from a minute displacement, go in two different directions.
The detection of passes according to these criteria often produces in
practice many parasitic passes, of weak amplitude, close to an extremum
of H. Most often, a minimal modification of altitudes in the DTM makes
such artefacts disappear. The replacement of a square mesh by a triangular
mesh would also annul a certain number of them. This purification of
the model is a prerequisite for a correct topographic modelling and an
easier extraction of the characteristic lines.
The main characteristic lines
From a global point of view, a characteristic line is a line of slope assuring
the sharing of the outflow of the streaming waters. The definitions of these
lines often present two variants, depending on whether they are understood
according to the real geomorphology, or according to the algorithms
used to detect them. For example, with the geomorphological meaning,
a thalweg is generally not formed at the beginning of the watershed of a
torrent, the opposite of what the determination algorithms may show, as
they may define a ‘theoretical’ thalweg that may climb up to the pass.
THE MAIN THALWEG
The thalweg can be determined by the journey of a stream between the
pass that is maybe at its origin, to its end naturally in the basin that it is
going to find on its journey, while following the line of stronger downward
slope.
THE MAIN CREST
Extraction of characteristic lines of the relief 255
The localization of every crest, in the same way, is achieved as being the
journey followed by an anti-streaming (i.e. reversed streaming, assimilated
to water that would go up exclusively along the line of stronger slope) from
a pass to a summit, while following the line of stronger ascending slope.
CONCLUSION ON THE MAIN CHARACTERISTIC LINES
Crests and main thalwegs constitute the main oro-hydrographic system
that relies completely on the preliminary determination of the passes.
Special attention must be paid to low and/or flooded zones such as marshes,
lakes and large flat valleys, in particular when automatic extraction is
concerned.
All goes well if a tracing of a crest started in a convex zone is constituted
in a convex zone up to the junction with another crest or up to a summit,

256 Alain Dupéret and Olivier Jamet
but problems arise if there is an extension in a concave zone. A symmetric
remark can be made for a thalweg. This justifies the definition and the
taking into account of new characteristic elements of the relief.
3.6.1.3 Definitions of remarkable elements of the relief
The contour line
Contour lines are the plane curves of the function Z H(x, y). Associated
to the selected and regularly spaced altitudes of an interval called equidistance
of curves, they are often used to provide the cartographic
representation of the relief, often with a set of edition spot heights distributed
on remarkable planimetric points. Beyond this cartographic setting,
the horizontals can become characteristic elements of the relief as soon as
it contains extents of water. Contours of ponds and the foreshores of seas
are typically lines that present a remarkable slope discontinuity in the altitude
function for large topographic areas.
The curve n 0
The horizontal curvature of contour lines can also become the object of
an analysis. The convention, of course, foresees that an observer who
constantly follows a contour line in the direct sense turns on his right in
convex ground (left in concave). Numerous difficulties, notably those bound
to the parasitic passes, can be avoided by considering the limit between
the concave and convex zones of the ground. While calling n the horizontal
curvature of contour lines, the curvature n 0 represents the limit
we look for. In principle, the pass is a part of this particular curve.
The secondary remarkable points
Points whose definitions follow correspond to places of null curvature.
THE THALWEG ORIGIN
To palliate annoyances mentioned previously concerning the main characteristic
lines, the high points of the curve n 0 will be taken as thalweg
origins.
THE END OF CREST
The crest ends will be defined as the low points of the curve n 0.

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REMARKS ON THE SECONDARY REMARKABLE POINTS
Other approaches than the one presented are possible, as the one that
would consist in taking all points for which the slope p is maximum; ends
of crest are indicated when n > 0, beginnings of thalweg by n 0, from the
secondary crest ends, while going up the long of the larger slope line up
to the junction with a main line.
REMARKS ON THE SECONDARY CHARACTERISTIC LINES
The reliable extraction of the characteristic elements has therefore a particular
importance, whose automation appears desirable, especially because
the manual extraction seems delicate. Indeed, in opposition to the acquisition
of level contour lines for which the z device is blocked at the time
of the acquisition, or to the seizure of nodes of a net for which the planimetric
position is imposed, the direct photogrammetric acquisition does
not show any systematism. The positioning freedom is large, extremely
correlated to the altimetric precision of pointing and intervenes in zones
that require a significant effort to be correctly described: vegetation in
thalweg bottoms, flat crests, etc.
3.6.1.4 Notions of drainage network and watershed
A drainage network is defined (Deffontaines and Chorowicz, 1991) as being
composed of ‘the set of the topographic surfaces situated below all neighbouring
high points, generally flowing out according to a direction. These
surfaces can contain water in temporary or permanent manner’. It includes:
• thalwegs: valley bottoms, narrow or large, with water or dry;
• closed endorheic or exorheic depressions such as marshes, sink-holes,
lakes.

258 Alain Dupéret and Olivier Jamet
To do some automatic extractions following this definition, several families
of methods are used on DTM, either by dynamic analysis of the streaming,
or by local analysis of the surface curvature.
In hydrology, the true catchment area relative to a point is defined as
the totality of the topographic surface drained by this point; it is therefore
a geographical entity on which the ensemble of water enters, due to
the rain, and shares and organizes itself to lead to a unique outlet in the
exit of a catchment area. As for the topographic catchment area relative
to a point, this is the location of the points of the topographic surface
whose line of larger slope passes by this point. There is not necessarily
coincidence of the two types of catchment areas, for example for karstic
reliefs where water that streams inside a catchment area can be found in
the exit in another catchment area because of losses and re-emergences.
In the same way, water that infiltrates the ground can meet the impervious
layers that direct it to water-tables participating thus in other
hydrologic basin balance. To finish, human activity generates obstacles or
reaches that often modify the natural logic of the stream.
As the topographic, geological and pedological properties of a catchment
area constitute some essential parameters for its survey, it is nesessary
to perform a reliable digital modelling of the relief, in particular of the
drainage network. In such a context, many digital indexes, more thematic,
are used to characterize a catchment area: the drained surface, lengths of
drainage, the perimeter, the distance to the outlet, the size of the drained
surfaces, densities and frequency of drainage, the indication of compactness,
the ratio of confluence or concentration, the Beven index, etc.
[Depraetère and Moniod, 1991].
3.6.2 Extraction of thalwegs from starting points
This method, named ‘structuralist approach’ by the author (Riazanoff
et al., 1992) is inspired by the physical model of water streaming on a
relief and proposes a dynamic method of determination of crest lines. The
tracing of lines is judiciously dynamic from the starting points chosen,
while following the line of larger slope up to arrive either in a border of
the zone, a local minimum or on an already drawn line. The algorithm
proceeds by two distinct steps. The first consists in describing completely
the network coming down from all main passes and following the largest
slope. The second applies to correcting shortcomings produced by depressions
while forcing the drainage toward the lowest pass.
The thalweg is defined as ‘concave place of water convergence’. The
crest is defined in a dual manner as ‘convex place of anti-streaming convergence’.
These two characteristic line types cross themselves in singular
points, mainly passes, but also the local extrema, the high points (local
maximum of a concave zone) and the low points (minimum local of a
convex zone).

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Extraction of characteristic lines of the relief 259
A constraint of initial progession is applied for the particular case of
the starting point. Three different advance constraints have been used for
this method, the description being made for the extraction of crests.
1 The algorithm of the stream: the constraint of advance is ‘to climb
according to the line of larger slope’, while choosing among neighbours
the one that presents the largest denivelation in relation to the
displacement among the neighbouring points. The starting point is a
pass. Thus the network obtained can be considered as too dense. The
detection is also meaningful for zones situated at a low altitude, if
compared to zones of average or high altitude.
2 The algorithm of the wanderer: from the local maxima, the constraint
of advance used here is ‘to go down towards points presenting a convex
slope change in one of the three directions (four minus the one of
origin)’. This process makes it possible to survey the main structures
but is very sensitive to the least disconnection that leads to the nonconsideration
of possible structure situated downstream.
3 The main pass algorithm adds up the information from the two
previous algorithms in order to select starting points susceptible of
generating the main characteristic lines. From the passes not marked
in the network obtained by the previous method, the constraint of
advance is ‘to climb according to the line of larger slope’. All marked
passes are passes not belonging to the network generated by the
climbing from the local minima on thalwegs; in fact, a pass will not
be marked if it is located on the extremity of a branch of the network.
The main crests are correctly marked. The principal massifs and hills
are marked.
The third method, using the first two, gives best results. The outlet is
searched for. Logically, the point of outlet is the lowest pass among those
from where come lines of outflow arriving at this depression. To improve
the method, the sense of outflow of the line from the outlet is reversed,
and the outflow continues on the other side of the pass. Other approaches
preserved the principle to apply a method of streaming according to the
line of larger slope, without trying to start again from particular points
such as passes. From every pixel, an outflow on the model is simulated
according to the nearest pixel of the line of larger slope.
3.6.3 Extraction of thalwegs by global outflow calculation
or accumulation
Methods that follow exploit the same operative definition of thalwegs as
techniques of progress previously presented: thalwegs, generated by
phenomena of natural erosion of the ground, are places of river passage,
assimilated to lines, understood this time as places where the pluvial waters

260 Alain Dupéret and Olivier Jamet
concentrate. This definition is no longer in order to perform a local extraction
of the network (either by local operators, or by following step by
step a given line), but to exploit the whole surface to determine lines on
which the strongest debits would appear in case of a uniform rain on the
site.
The representation by a regular rectangular mesh is the one that leads
to the simplest algorithms and will be the only one treated in this section
(explanation data are even more strictly restricted to the square meshes).
We will even speak of pixels (by reference to the terminology of Image
Processing) to designate the points of the mesh.
In spite of these limitations, the methods present here the two interests
of offering continuous line extraction and permitting some extremely simple
implementations. As the results are very realistic on all land with a marked
relief, these methods are among the most used.
3.6.3.1 Calculation of the drained surfaces
If we suppose there is a uniform rain across the whole of the land, the debit
of the permanent regime is in any point proportional to the cumulative
surface upstream of this point. Used in its discrete approximation, this
property helps us calculate, for every pixel, its drained surface as the sum
of the surface of a mesh (influence of the pixel considered) and the drained
surfaces of pixels neighbouring, uphill, the considered pixel. Thalwegs are
then local extrema places, on curves of constant altitude, of the drained
surfaces. (See Figure 3.6.1.)
This definition gives rise to several algorithms, depending on whether
one defines neighbourhoods in 4 or in 8-connexity, according to the way
the relation ‘being uphill of’ is defined, a relation that we call relation of
outflow, and according to the technique used to extract lines of thalwegs
from the drained surface image.
We will restrict the explanation to the 4-connexity topology. The use
of the 8-connexity, sometimes recommended, causes the problem of a incoherent
topology: paths of outflows materialized locally by relations of
neighbourhoods cross themselves, which doesn’t correspond to a coherent
physical model. Let us note that the techniques presented below are easily
transposable in 8-connexity, maybe to the cost of an a posteriori correction
procedure of resulting artefacts, which are always local.
The choice of the outflow relation leads to the distinction between two
families of algorithms, presented briefly here. The techniques of extraction
of thalwegs lines themselves, that can be chosen independently of the algorithm
used for the calculation of surfaces, are presented in a different
section.
The simplest approach consists in considering that every pixel cannot
be uphill of more than one pixel among its neighbours. The downstream
pixel will be chosen, on the one hand, so that its altitude is strictly lower

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Extraction of characteristic lines of the relief 261
than that of the pixel considered, and on the other by a criterion of slope
(the outflow of waters following the steepest slope).
This formulation ensures that the graph of the outflow relation is without
closed cycle, in other words that this relation defines a tree on the DTM.
(See Figure 3.6.2.)
The calculation of drained surfaces can be treated with a recursive algorithm
or, more elegantly, using the natural order of altitudes to start the
calculation with the highest points, and accumulating drained surfaces in
one pass.
In the formulation of Le Men (Le Roux, 1992), the downstream pixel
is the pixel for which the slope is steepest. This choice is operative on
hilly landscapes (strong local variations of slopes), but produces drifts
on smooth surfaces, bound to the quantification of outflow directions: the
algorithm presents a defect of isotropy, a function of the direction of
the mesh.

262 Alain Dupéret and Olivier Jamet
Figure 3.6.2 Tree of the outflow relation on a DTM.
Contour lines
Pixel considered as an
area
Flow link
(from up toward
downstream
The method of Fairfield (Fairfield and Leymarie, 1991) palliates this
defect by proposing a random choice of the pixel downstream between
the two pixels materializing the two larger slopes, the probability of choice
of one of the two points being defined as proportional to the slope. This
rule guarantees the identity of the mean direction of the pixel downstream
and of the true direction of the steepest slope on a tilted plane, whatever
is the orientation of the mesh. (See Figure 3.6.3.)
Calculation on the graph of outflow
The anisotropy (or the sensitivity to the direction of the mesh) resulting from
the unique choice of the downstream pixel the steepest slope is the origin
of a second family of approaches. Considering that the average direction of

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Extraction of characteristic lines of the relief 263
Figure 3.6.3 Outflow relation on a planar surface: (a) highest slope choice: the
flow drifts away from the real direction; (b) two higher slopes
random choice (Fairfield method): the average flow follows the real
slope.
the outflow must remain faithful to the real direction of the steepest slope,
Rieger (1992) proposed to take into account, as pixels downstream of a
given pixel, all neighbours of lower altitude, and to propagate the surface
drained of a pixel to its downstream pixels according to the slope values.
In this formulation, the relation of outflow defines on the DTM a graph
that is not other than the graph of neighbourhood oriented in the direction
of decreasing altitudes (with exceptions of altitude equality, which we will
return to). This oriented graph being without cycle, as the tree of outflow
discussed previously, the algorithm of drained surface calculation can proceed
in the same way (propagation of drained surfaces in the direction of
decreasing altitudes).
This empiric formulation, which has the advantage of producing a more
regular image of drained surfaces than Fairfield’s method, does not,
however, lead to an isotropic algorithm. A variant in 8-connexity due to
Freeman (1991), founded on an ad hoc formulation of transmitted surfaces,
leads to a better isotropy on surfaces of revolution, but not in the general
case.
Jamet (1994) showed that, in the formulation of Rieger, the calculated
drained surface is considered to be the calculated debit in the permanent
regime, under a uniform rain on the whole DTM, and for a modelling in
which pixels are assimilated to cells communicating by their lateral sides.
For such a modelling, this debit depends on the orientation of the mesh
in relation to the real slope of the ground. The simple calculation of the
debit by unit of length orthogonal to the slope, deduced from the debit
of the mesh and slopes to its neighbours, insures the exact isotropy of the
result. Besides, on regular surfaces, this calculation of isotropic debit
permits a rigorous definition of the convexity of the surface, the gradient
of this debit being equal to the unit on the plane, lower on concave and
greater on convex surfaces. (See Figure 3.6.4.)

264 Alain Dupéret and Olivier Jamet
Figure 3.6.4 Drained surfaces computed on a spherical cap: (a) highest slope
flow; (b) Fairfield method; (c) Rieger method; (d) Freeman method;
(e) Jamet method; (f) theoretical expected result; (g) shows slight
anisotropic effects on non-circular symmetric surfaces with Freeman
method; (h) shows on the same surface as (g) the results of Jamet
method.
Extraction of thalwegs
In all previous methods, the result of the phase of surface accumulation
(or of calculation of the debit) leads to a map superposable on the DTM
on which the researched thalwegs correspond to local extrema orthogonally
to the calculated slope on the DTM.
Three types of techniques are used. The first relies on the classic techniques
of image processing. Considering that the image of surfaces drained
(or of the debit) is contrasted enough (or can become so after application
of a digital skeletonization process), the binary mesh map of thalwegs is
obtained by simple threshold of surfaces. The threshold corresponds
to the minimal size of catchment area able to feed a drain. A vector representation
of the network is deduced by a classic technique of vectorization
(Le Roux, 1992). This method remains more suitable to approaches by
outflow tree, as far as only these guarantee that the surface remains strictly
increasing from the upper to the lower part of a drain (and therefore that
the threshold won’t be able to break their connectivity).
The second uses the tree of outflow as it has been defined previously,
and remains therefore also more adapted to the corresponding family of
methods. The tree of outflow is a vector structure linking the set of pixels
of the DTM. The extraction of the thalweg network consists therefore

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Extraction of characteristic lines of the relief 265
Figure 3.6.5 Drained surfaces computed on a DTM: (a) DTM (shaded);
(b) highest slope algorithm; (c) Jamet’s algorithm.
just in selecting a sub-tree of the outflow tree (Le Roux, 1992). The criterion
of selection will be in the same way as previously a simple threshold of
the drained surface (with the same guarantee of topological consistency).
The third constructs the vector representation of thalwegs in a recursive
way, while starting with stronger debit drains. Except in an exceptional
case, any thalweg goes either in another thalweg, or outside the treated
zone. One can therefore count points of thalwegs’ exit by carrying out an
inventory of the local extrema of the surface drained on the edge of the
DTM, then go up thalwegs following this local extremum uphill (until the
drained surface goes below a threshold value). Recursively, new starting
points can be detected along every thalweg, looking for local extrema of
the gradient of the drained surface, which correspond to the junction of
an incoming drain (Rieger, 1992).
Figure 3.6.6 Thalweg extracted by the highest-slope method (a) and by Jamet’s
method (b) superimposed on a shaded DTM.

266 Alain Dupéret and Olivier Jamet
In any case, the obtained detections can contain artefacts. The too-short
drains are therefore either ignored (Rieger, 1992), or eliminated a posteriori
by too-short bow suppression in the obtained network or by morphological
ebarbulage.
3.6.3.2 Considerations on the artefacts of the DTM
The above-described methods suppose on the one hand that outside of
natural basins of the landscape and the sides of the site, any point of the
DTM possesses at least a neighbour of lower altitude, and on the other
hand that the direction of the ground slope is defined everywhere. This
last condition being equivalent to the absence of a strictly horizontal zone,
one can speak of an hypothesis of strict growth of the DTM between the
natural outlets of thalwegs and the summits.
This hypothesis is never verified. The step of sampling data indeed limits
the possibilities of representation of the present shapes on the surface, and
in particular of the steep-sided valleys: so, along a thalweg crossing a valley
whose width shrinks until a dimension commensurable with the sampling
step, the altitude won’t be able to vary in a monotonous way and one
will observe on the DTM a local minimum of altitude upstream of the
steep-sided setting. In the same way, the step of quantification in altitude
fixes a lower limit to the representable slopes on the DTM: any weaker
slope zone will appear as a strictly horizontal zone.
To these effects contingent to the discrete representation of data, some
effects particular to the used source can be added: noise of acquisition on
raw data generating local minima of the altitude, shortcomings of interpolation
(for example, creation of horizontal zones for lack of information
in the interpolation of contour lines), consideration in the representation
of elements not belonging to the topographic surface (for example, vegetation,
for the DTM produced by automatic image matching, that can
cause an obstruction to a thalweg) . . .
For grounding these artefacts, one supposes on the one hand that the
ground doesn’t include a strictly horizontal zone – their process will consist
then in inferring the sense of the outflow from their environment – and
on the other hand that only the important basins are meaningful – this
notion is specified farther.
Faced with such problems, some authors have proposed solutions based
on local techniques: these approaches result in giving an inertia to the
outflow, which will permit it to clear zones of null slope, or even to go
up the slope to come out of the artificial basins (see for example (Riazanoff
et al., 1992) in the case of methods by progression). These methods don’t
permit an efficient control of the restored thalwegs’ shape. We will limit
the following, therefore, to methods based on a larger analysis of shapes
of the relief.

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Extraction of characteristic lines of the relief 267
Horizontal zone process
The horizontal zones can be solved in two manners: either one considers
outflows as indeterminate on their extent, or one wants to define
them.
In the first case, the horizontal zones are treated as lakes, fed upstream
by the neighbouring pixels of larger altitude (that one will call input points),
and opened on the neighbouring pixels of lower altitude (that one will
call output points). Practically this option means calculating the relation
of outflow, no longer on the topology of the usual neighbourhood induced
by the mesh of the DTM (4 or 8-connex), but on a more elaborate topology,
in which the nodes may be either points (pixels) or surfaces (the horizontal
zones) – while relations of the neighbourhood remain relations induced
by geometry.
At the end of the process of thalwegs extraction, the horizontal zones
included in the tracing can be replaced by bows, whose geometry can be
calculated, for example, by squeletization of these surfaces.
In the second case, the choice of the outflow sense on horizontal
zones is subordinated to their shape and their environment. The simplest
technique consists in forcing senses of outflow from input points toward
output points. For that, one can consider for example that a pixel of a
flat zone is uphill of one of its neighbours if and only if its distance to
the nearest exit point is greater than that of this neighbour. The distance
used can be a discrete distance, calculated by dilation of the exit border,
constrained by the extension of the horizontal area. This approach can be
completed by a consideration of the shape of the zone: considering that
the thalweg (non-observable on the DTM) must cross the centre of the
zone, one can for example subordinate directions of outflow to the whole
of the border of the zone, that is to say simultaneously to the distance to
input points and the distance to output points as well. This last option
has the advantage of also being valid if the horizontal zone does not possess
an output point.
Figure 3.6.7 Flow topology induced by a flat area.

268 Alain Dupéret and Olivier Jamet
These types of calculation mean to accord a digital value to every
pixel of the horizontal zone, which can be chosen in order to respect the
required property of strict growth on the DTM. This set of values can
then be assimilated to the decimal part of altitudes in calculations of
slope.
Process of basins
One designates under the term of basin the catchment areas of the local
minima of the DTM, which in most cases are correlated to artefacts. The
correction of these artefacts consists in searching for one or many points
of exit to the border of these catchment areas, and to force the outflow
of the local minimum toward these points of exit (and therefore in the
sense opposite to the slope).
The position adopted by most authors consists in minimizing the incoherence
of the outflow, that is to say to search for the points of exit
whose height over the local minimum is the weakest possible. All basins
not being necessarily artefacts, this process will generally be controlled
by a threshold on this height – or denivelate, the basins whose exit are
higher than the threshold being preserved (that is to say considered significant).
The search for the points of exit of a basin cannot, however, be done
independently of its environment: in complex situations, where numerous
basins are neighbouring, the local determination of points of exit can lead
to the simple fusion of neighbouring basins forming a new large-sized
basin. If this process remains foreseeable while applying it recursively until
disappearance of all non-meaningful basins, it can be very expensive. One
has therefore rather to formulate the problem of the basin resolution like
a search for a global minimum to the whole site. An economic solution –
as it produces an algorithm of low complexity – consists in defining the
total cost of the basin resolution as the sum of denivelates to cross in the
sense inverse to the slope. Indeed, the sum of local minima altitudes being
a constant of the problem, the minimization of the sum of denivelates is
equivalent to the minimization of the sum of altitudes of the chosen exit
points. The choice of points of exit is thus independent of the sense of the
outflow, and can be operated by a simple search for the minimal weight
tree in the dual graph of the basin borders, where each bow is valued by
the minimal altitude of the corresponding border – that is to say the altitude
of the existing lowest pass between each neighbouring basin pair.
The sense of the outflow can then be calculated recursively in the obtained
tree, from the known exit points (sides of the site or meaningful basins).
(See Figure 3.6.8.)
Once the output points are chosen, as in the case of the horizontal zones,
the process of basins can give rise to a simple topological modification or
to a geometric process of the DTM.

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Extraction of characteristic lines of the relief 269
Figure 3.6.8 Search of the basin exit: the simple choice of the lowest pass leads
to the fusion of R 1 and R 2 without giving them an outlet. A global
search has to be performed in the graph of neighbourhood of the
basin.
Among the topological processes, the two most obvious techniques
consist in adding a relation of outflow between the local minimum of every
basin and its pass of exit – with the drawback of producing non-connex
thalwegs at the end of the process – either to reverse the sense of the
outflow on pixels leading from the local minimum to the pass of exit
following the steepest slope (Fairfield and Leymarie, 1991). This last technique
can however be used only in the case of accumulation calculations
on the outflow tree: the inversion of the sense on only one path creates
indeed some cycles on the graph of outflow, and does not permit the other
techniques to be used any longer.
The most current geometric process consists in modifying the geometry
of the DTM to construct an exit path of constant altitude, by searching for
a pixel of lower altitude than the local minimum downstream of the exit
pass, by levelling of the DTM on the path of steepest slope joining these
two pixels (Rieger, 1992). This last solution is more adapted in the case of
accumulation techniques on the entirety of the graph of outflow.
Let us note finally that the order of process of the horizontal zones and
the basins is not irrelevant: as the process of basins is leading to a modification
of outflows on the DTM, it must evidently be applied before the
process of horizontal zones.
3.6.3.3 Annex results
The methods presented in this section have the advantage of giving
access to a description of a topography richer than the simple network of

270 Alain Dupéret and Olivier Jamet
Figure 3.6.9 Watershed extracted by an outflow method: (a) DTM (shaded); (b)
thalweg network; (c) watersheds (represented by various grey levels,
and their boundaries in white).
thalwegs. The calculation of the horizontal zones and basins, understood
as artefacts of the DTM, provides an indicator of its quality. The calculation
of the drained surface offers a natural hierarchy of the network
of thalwegs, which can prove to be useful in numerous applications. The
materialization of outflows on the whole surface permits the direct calculation
of catchment areas associated to each thalweg or every portion of
thalweg (for example, by simple labelling of its pixels uphill in the outflow
tree). This decomposition of the surface is used extensively, in particular
for the physical modelling of flood phenomena (Moore et al., 1991), but
also for the cartographic generalization (Monier et al., 1996). Finally, the
network of crests, subset of catchment areas borders, is also accessible by
this type of technique, either that one adapts algorithms of accumulation
to calculate a function of adherence to catchment areas on the same mode
as the calculation of the drained surfaces, or that one uses directly calculated
catchment areas to extract their borders by techniques of vectorization.
3.6.4 Extraction of thalwegs from local properties
This family of methods was historically the first to be used (Haralick,
1983). For this algorithm and those that followed, the common idea is to
search, on every pixel of the DTM, independently of results on the neighbouring
pixels, to see if the current point verifies a certain relation with
its environment; in which case, it receives a stamp that identifies it as a

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Extraction of characteristic lines of the relief 271
point of crest or thalweg. Only some methods, considered as representative,
will be presented below.
3.6.4.1 By analysis of the discrete representation
The surface is analysed here in a discrete way. Kim’s method (1986) is the
more often evoked. The algorithm proceeds by a scan of the DTM according
to X and Y in order to identify elementary geomorphologic shapes.
With this method, the algorithm scans the DTM from left to right, then
from top to bottom. During the sweep, characters are accorded to pixels
(of the DTM) successively according to the nature of the slope that is
between them. A threshold of altitude differences is applied to define the
horizontal surfaces. Transitions between points are qualified according the
following rules:
• the passage of a point to a higher one is represented, e.g. by the character
‘’;
• the passage of a point to a lower one is represented by the character
‘’;
• the passage without change of the level of a point to a higher one is
represented by the character ‘’.
The interpretation of the shapes of models (images constituted by the
three characters , and ) produced by two scans makes possible a
first analysis, according to the scan profile, of the local morphology of the
ground. The analysis relies on successions of slope characters ‘’, ‘’, ‘’,
for example, if a ‘’, is followed by a ‘’, it indicates the presence of a
steep-sided thalweg, while several ‘’ followed by several ‘’ followed
again by one or several ‘’ could mean a large valley bottom or the flat
bottom of a basin.
The superposition of the two scan models, in the longitudinal and
transverse sense, permits one by comparing the information, to deduce
characteristics of the local morphology in the two dimensions.
Thus the obtained model allows, after an ad hoc filtering, elements of
the main characteristic lines network to be recovered.
In certain cases, shapes are not very clean, in particular in the flat zones.
In addition, the connection of the network is not always satisfactory, a
certain number of segments remaining isolated.
3.6.4.2 By analysis of a continuous representation
The surface is assumed to be continuous, or continuous by pieces so as
to provide an analytic expression of the surface. The function representative
of the altitude must make it possible to give an account of the different
discontinuities due to the terrain:

272 Alain Dupéret and Olivier Jamet
• slope, cliffs directly bound to the altitude;
• lines of slope rupture (concavity, convexity);
• line of curvature rupture.
On neighbourhoods of given size, the continuity of the slope can be
obtained by junction of parabolic bows and that of the curvature by the
utilization of cubic bow. Several methods explored this possibility; Haralick
(1983) makes the analysis with the help of a model using some bi-cubic
functions. The method that will be presented (Dufour, 1988) relies on the
hypothesis that the ground can be modelled with the help of a Taylor
series, which will be limited here to the order 2, which permits one to
describe a sufficiently large number of phenomena.
Z H(X,Y) H(X 0 ,Y 0 ) ax by (cx 2 2dxy ey 2 ) ,
where x X X 0 and y Y Y 0 are considered small.
Formulae of determination of coefficients of the polynomial depend on
the chosen mesh. The square configuration will be used here and the coefficients,
calculated by the least squares method are expressed in the
following manner (Dupéret, 1989):
H 0 5H 0
9
2
9 (H 2 H 4 H 6 H 8) 1
9 (H 1 H 3 H 5 H 7)
a 1
6 (H 1 H 7 H 8 H 3 H 4 H 5 )
b 1
6 (H 1 H 2 H 3 H 5 H 6 H 7)
c 1
3 (H 8 H 4) 2
3 (H 2 H 6) 1
3 H 1 H 3 H 5 H 7 2
3 H 0
d 1
4 (H 1 H 5 H 3 H 7)
e 1
3 (H 2 H 6) 2
3 (H 8 H 4) 1
3 H 1 H 3 H 5 H 7 2
,
3 H0 where H i is defined according to Figure 3.6.10.
The horizontal curvature is a very interesting variable, which uses all
first and second derivatives of the altitude function. It takes very strong
negative values in thalwegs, remains weak in the regular sides and becomes
very strongly positive along the crests.
The horizontal curvature at point (x, y) (0, 0) of contour lines is
expressed according to the coefficients above:
1
2

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Extraction of characteristic lines of the relief 273
1
8
Figure 3.6.10 Numerotation of the points of the neighbourhood, of altitude
H 0, H 1 ... H 8.
N .
The same principle is applicable to the calculus of all variable geomorphometric
types expressed according to derivatives of the altitude function:
slope, curvature of level lines, curvature of slope lines, Laplacian, quadratic
mean curvature, total curvature, etc.
2abd cb2 ea2 (a2 b2 ) 3/2
?
R2
?
R1
Figure 3.6.11 Curvature radius R 1/ N in two points of the ground.

Figure 3.6.13
Figure 3.6.12
Representation of N
(from the darkest to the
lightest grey, the thalwegs,
the crests, then the
intermediate zones) with
the superimposition of
contour lines.

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3.6.4.3 Synthesis
The search for points of the characteristic lines independently from each
other eludes the very notion of characteristic line. If the acquisition
mode and the density are appropriated, then these methods can provide
a posteriori these lines. However, in the main, the extracted network is
non-connex with sometimes segments of non-negligible thickness. Even if
they are very robust, these algorithms very rarely restore completely
the logic of a hydrographic network. The identified points often form
dispersed segments, therefore non-connex, and these sets of points have a
variable thickness.
Some mixed methods were also set up. Thus, the algorithm of Ichoku
(1993) proceeds by combination of Kim’s and Riazanoff’s algorithms and
provides a hierarchized and reasonably connected network. Basins are eliminated
according to the principle of the inversion of the sense of the
drainage. Although the general connection of the network is superior to
the two basic methods used, some parasitic networks subsist.
3.6.5 Numerous applications
Extraction of characteristic lines of the relief 275
Examples that follow are by no means exhaustive. They are mentioned
merely to show that some varied applications can be built on data produced
by the above mentioned methods. Some do not require the connection of
segments that compose the network. The mastery of the representation
of characteristic lines network is the basis of various measures on watersheds.
3.6.5.1 The hierarchization of a hydrographic network
The networks of thalwegs produced by different methods can allow the
hydrologists to build a hierarchical classification of segments composing
the detected network. Two methods among all those possible are presented
here.
The first use by Riazanoff is introduced by Shreve (1967). A segment is
a part of the active network of a point source to a confluence, or of a
confluence to another confluence. Every segment possesses a hierarchical
value that is the sum of the hierarchical values of immediately upstream
segments, segments that are the most upstream (descended of a source)
receiving the hierarchical value 1. (See Figure 3.6.14.)
A second method, due to Horton (1945) and improved subsequently,
establishes the hierarchy in the following way:
• rivers not having even received an affluent are of order 1;
• rivers having received at least a river of order 1, therefore 2 rivers of
order 1 are of order 2;

276 Alain Dupéret and Olivier Jamet
1
1
1
3
1
Figure 3.6.14 Example of network in the classification of Shreve.
1
1
1
2
2
1
Figure 3.6.15 A similar network in the classification of Horton.
3
2
• rivers having received at least a river of order 2, therefore 2 rivers of
order 2 are of order 3;
• and so on.
(See Figure 3.6.15.) The final order of the outlet river of a catchment area
has a comparable value from a basin to the other, provided that they result
from surveys of the same scale.
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Extraction of characteristic lines of the relief 277
It is then possible for the user to establish relations of comparison between
the order, the designation of the river and the surface of catchment areas.
For example, the denomination ‘large river’ will be reserved to segments
of order 7 and 8, with associated catchment areas of a surface between
10,000 and 100,000 km 2 .
With the help of this hierarchization of networks, the user can also use
thresholds on the order of segments in order to limit some parts of the
drainage network.
3.6.5.2 The cartographic smoothing
Despite all precautions, the filtered DTM presents softer ground shapes in
comparison to what they should be. To limit the deterioration of terrain
shapes, one may therefore use a cartographic smoothing process that has
to determine as automatically as possible the zones of the DTM that correspond
to the characteristic lines of the ground.
For example, the program used in IGN-F calculates a digital model of
horizontal curvature in the DTM (performing a classification in five
domains) with homogeneous geomorphometric properties describing highly
convex zones (crests) up to strongly concave zones (thalwegs).
Parameters of adapted smoothing can then be applied in an uniform
way on each of its zones to get the contour lines smoother, but preserving
a good description of the terrain shapes. (See Figure 3.6.16.)
Figure 3.6.16 Comparison of level curves restored by hand (in grey) and
cartographically smoothed (in dark grey).

278 Alain Dupéret and Olivier Jamet
3.6.5.3 Automatic cut-off of watersheds
As an indispensable component to the rational management of digital data
in GIS, the limits of watersheds has for a long time been digitized by hand
before being inserted digitally. The first studies in automation started in
1975. One of the first methods (Collins, 1975) proposes to classify all
points of the DTM by increasing order of altitude. The lowest point is an
outlet of the watersheds; if the second lowest point is not connex to it, it
means therefore that it belongs to another basin. The provided results are
good but are unstable with a real DTM where objects on the ground, the
plane zones and irregularities of thalwegs’ profiles destabilize the procedure
of detection.
Since then numerous methods have been studied, trying to extract from
the DTM the points presenting the property of adherence to a line of crest.
The different strategies used to make the set of points connex and of unit
thickness have most of the time stumbled on the discontinuous characters
of lines obtained and the problem of local minima. The assimilation of
the main and secondary crest lines in methods of non-hierarchical detection
puts the problem of identification of the real lines of water sharing.
The theory of the mathematical morphology constituted an efficient and
original contribution to this type of survey while permitting an automatic
method of catchment areas cut-off to be finalized (Soille, 1988).
3.6.5.4 Manual editing of DTM
The characteristic line extraction as it has just been presented is often
disrupted in practice by the presence of micro-reliefs, artefacts of calculation,
as small crests, passes or aberrant basins, without physical reality.
The elimination of these topographic anomalies can be performed by
replacing the series of elevations, in the considered thalweg, by a new set
of data, obtained by a controlled diminution of the values. It is easy but
poses the problem of other altitude modifications to the neighbourhood
of the thalweg. The step of interactive manual correction proves to be, for
the meantime, still indispensable. On its duration depends the economic
opportunity to make these corrections by hand. At best, three DTM editors
are accessible in some software:
• A punctual editor, intended to modify only one altitude at a time (used
rarely).
• A linear editor working in such a way that the operator indicates interactively
a 2D or 3D axis with a chosen influence distance. Inside the
concerned zone, altitudes are resampled according to hypotheses made
on the desired profile of ground perpendicularly to the axis indicated
by the operator (profile in U, in V, linear, bulldozer . . .). This editor
is useful for suppressing altimetric prints of hedges in the DTM, or
when characteristic lines and/or a hydrographic network is available.

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Extraction of characteristic lines of the relief 279
Figure 3.6.17 In black: example of linear object that can give rise to updating of
the profile of the ground in the DTM among the four possibilities
and distance of interpolation (D) to the axis of the object: uniform
interpolation, in U, in V or some in bulldozer. Surfacic processes
can be applied to objects systematically known by their perimeter:
a clear hydrographic surface (in the bottom-left corner, surrounded
by a clear line) can be given a rigorously constant altitude, a forest
(right, surrounded by a clear line) can receive a bias corresponding
to the mean height of the trees.
• A surfacic editor that allows the operator to select a process to apply
to altitudes situated inside a polygon: various resamplings, force to a
constant level, application of a bias, parametrable filtering of the
objects over the ground . . . .
The manual correction operations are shorter and more efficient if the
DTM quality is good. At this step, in spite of everything, the user will not
avoid some topographic anomalies, like the thalweg perched in the convex
zone, the crest enclosed in a concave zone or the delta of a river in which
the stream passes from convergent to divergent zones.
3.6.5.5 Toward a partition of the ground in homogeneous
zones?
The different adopted definitions lead to a partition of the domain in
catchment basins that must be completed to achieve morphologically a
separation in homogeneous domains.
The decomposition of the ground in homogeneous zones under shape
of curvilinear triangles is foreseeable. It represents immediately a finality

280 Alain Dupéret and Olivier Jamet
for the topographer and a way toward a rational generalization of the
relief. The junction between two neighbouring triangles takes place along
a sinuous curve corresponding to singularities of the function altitude in
general. Such a model is attractive because it inserts without difficulties
delicate topographic situations such as:
• valleys with a low slope with a sinuous course, and
• rocky-toothed cliffs,
which required a decomposition of the domain into numerous facets.
Every curvilinear triangle includes a parametric representation with a
limited number of parameters (e.g. 30 coefficients for a parametric system
of cubic type). The value taken by these functions in the border of zones
makes it possible to recover the curvilinear character of separation lines.
In the curvilinear domain (ABC), X, Y and H are represented by cubic
functions of the barycentric coordinates of the ABC triangle. Cubic functions
X(, , ), Y(, , ), H(, , ) include each ten independent
parameters that can be defined by values of (X, Y, H) to the three summits,
as well as in two points on every curvilinear side and one central point.
and
area (MBC)
area (ABC)
1
.
area (MAC)
area (ABC)
area (MBA)
area (ABC)
Separation lines are to be looked for giving priority to where there are
obvious discontinuities:
• of the function altitude (slope, cliff);
• of the derivative of the slope (crest, steep-sided thalweg);
• of the curvature (slope rupture).
The convenient exploitation of such a model presents various difficulties
whose major problem is the reliable automatic determination of lines of
homogeneous zone separation.
3.6.5.6 Complementary approach
The automated extraction of the characteristic line networks is of course
a privileged way of knowing the surface of the land, which comes in
complement to other approaches, for example: the determination of surface
envelopes (Carvalho, 1995). A surface envelope is a general, schematic and
theoretical model of the relief that makes it possible to recover, in certain
cases, the general lines of a situation of maturity of the relief, and to

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analyse the links between the present and old topographies. The surface
envelope relies on the high points of the relief of a region, so as to eliminate
irregularities of the topographic surface coming from the linear
erosion of rivers. Indicators of surface thickness either eroded or erodable
can be deduced from differences between DTM and the surface envelope
to provide some useful elements to the evaluation of erosion balances.
The automatic detection of summit points is considered here therefore
like a tool serving the development of a numeric representation of surface
envelopes while giving points of passage. It is followed by a phase of
construction of the surface. The practice shows that the automation
of this determination is justified when the DTM mesh is adapted to the
land. The simultaneous knowledge of networks of thalwegs and surface
envelopes allows the imperfections of the thalwegs network in relation
to the summit surface envelopes to be determined (direction of the thalwegs
network not compliant with the lines of steepest slope of the surface
envelopes).
References
Extraction of characteristic lines of the relief 281
Carvalho J. (1995) Extraction automatique d’informations géomorphométriques
(réseaux et surfaces enveloppes) à partir de modèles numériques de terrain. Ph.D.
Thesis, Université de Paris 7.
Chorowicz J., Parrot J.F., Taud H., Hakdaoui M., Rudant J.P., Rouis T. (1995)
Automated pattern-recognition of geomorphic features from DEMs and satellites
images Z, Geomorph. N.F. (Berlin), Suppl. Bd101, pp. 69–84.
Collins S. (1975) Terrain parameters directly from a digital terrain model, Canadian
Surveyor, vol. 29, no. 5, pp. 507–518.
Depraetère C., Moniod F. (1991) Contribution des modèles numériques de terrain
à la simulation des écoulements dans un réseau hydrographique, Hydrol.
Continent. vol. 6, no. 1, pp. 29–53.
Dufour H.M. (1977) Représentation d’une fonction par une somme de fonctions
translatées, Bulletin d’information de l’IGN, no. 33, pp. 10–36.
Dufour H.M. (1983) Eléments remarquables du relief – définitions numériques utilisables,
Bulletin du comité français de cartographie, no. 95, pp. 57–90.
Dufour H.M. (1988) Quelques idées générales concernant l’établissement et
l’amélioration des Modèles Numériques de Terrain, Bulletin d’information de
l’IGN, no. 58, pp. 3–18.
Dupéret A. (1989) Contribution des MNT à la géomorphométrie, Rapport de
stage, DEA SIG, IGN – IMAGEO.
Fairfield J., Leymarie P. (1991) Drainage network from grid digital elevation models,
Water Resources Research, vol. 27, no. 5, May, pp. 709–717.
Freeman T.G. (1991) Calculating catchment area with divergent flow based on
regular grid, Computer and Geosciences, vol. 17, no. 3, pp. 413–422.
Haralick R.M. (1983) Ridges and valleys on digital images, Computer Vision,
Graphics and Image Processing 22, pp. 28–38.
Horton R.F. (1945) Erosional development of streams and their drainage basins:
hydrophysical approach to quantitative morphology, Geological Society of
America Bulletin, vol. 56, pp. 275–370.

282 Alain Dupéret and Olivier Jamet
Ichoku C. (1993) Méthodes automatiques pour l’analyse et la reconnaissance des systèmes
d’écoulement en surface et dans le sous sol. Thesis, Université de Paris 6.
Jamet O. (1994) Extraction du réseau de thalwegs sur un MNT, Bulletin d’information
de l’IGN, no. 64, pp. 11–18.
Kim Y.J. (1986) Reconnaissance de formes géomorphologiques et géologiques à
partir de modèles numériques de terrain pour l’exploitation de données stéréoscopiques
Spot. Ph.D. Thesis, Université de Paris 6.
Le Roux D. (1992) Contrôle de la cohérence d’un réseau hydrographique avec un
modèle numérique de terrain, Rapport de stage, Laboratoire COGIT, IGN, Saint-
Mandé, France.
Le Roux D. (1993) Modélisation des écoulements sur un modèle numérique de
terrain – Applications aux crues et inondations du 22/09/89 à Vaison la Romaine,
Engineer End of Study Memoir, ESGT, Le Mans, France.
Monier P., Beauvillain E., Jamet O. (1996) Extraction d’éléments caractéristiques
pour une généralisation automatique du relief, Revue Internationale de Géomatique,
vol. 6, no. 2–3, pp. 191–201.
Moore I.D., Grayson R.B., Ladson A.R. (1991) Digital terrain modelling: a review
of hydrological, geomorphological and biological applications, Hydrological
processes, vol. 5, pp. 3–30.
Riazanoff S. (1989) Extraction et analyse automatiques de réseaux à partir de
modèles numériques de terrain. Contribution à l’analyse d’images de télédétection.
Ph.D. Thesis, Université de Paris 7.
Riazanoff S., Julien P., Cervelle B., Chorowicz J. (1992) Extraction et analyse
automatiques d’un réseau hiérarchisé de thalwegs. Application à un modèle
numérique de terrain dérivé d’un couple stéréoscopique SPOT, International
Journal of Remote Sensing, vol. 13, pp. 367–364.
Rieger W. (1992) Automated river line and catchment area extraction from DEM
data, ISPRS Congress Commission IV, Washington DC, August, pp. 642–648.
Shreve R.L. (1967) Infinite topologically random channel networks, Journal of
geology (Chicago), vol. 75, pp. 178–186.
Soille P. (1988) Modèles numériques de terrain et morphologie mathématique:
délimitation automatique de bassins versants, Engineer End of Study Memoir in
agronomy, orientation ‘génie rural’, Université catholique de Louvain la Neuve,
Belgium.
3.7 FROM THE AERIAL IMAGE TO ORTHOPHOTOGRAPHY:
DIFFERENT LEVELS OF RECTIFICATION
Michel Kasser, Laurent Polidori
3.7.1 Introduction
The very principle of an image acquisition, which means a conical perspective
for specialists, implies that a photographic image is not generally
superimposable to a map. It is partly due to the existing reliefs in the
observed object, and to the fact that even for an object that would be
rigorously plane, the optical axis has no reason to be precisely perpendicular
to this plane. For a very long time, techniques producing the

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controlled distortions of photographs have been developed in order to give
these images a comparable metrics to that of a map. These techniques can
be conceived at very elaborate levels, according to the requested quality.
Rigorously speaking, only when the correction is perfect is the product
obtained called orthophotography, but there are many intermediate solutions,
that one uses to get rectified images. Here we aim to clarify the
different levels possible, which have some very different costs, and corresponding
large differences of precision.
3.7.2 What is an orthophotography?
From the aerial image to orthophotography 283
The orthophotography is a picture (generally aerial) that has been geometrically
rectified to make it superimposable in any place on a map, possibly
with enriched graphic additions. These additions can originate either from
external information (administrative limits, toponyms, etc.), or from the
interpretation of the image itself (in order to ease its use: drawing of roads,
of building contours, etc.). If one compares it with classic cartography,
the orthophotography differs by the absence (that can be total) of most
phases of interpretation and drawing. As such tasks always require an
important human added value, the possibility of suppressing them permits
therefore an almost total automation of the process: it is through the
considerable reduction of costs and delays obtained that digital orthophotography
became a product more and more current, capable of completely
replacing the traditional cartography.
The process of manufacture necessarily implies knowing two data sets:
parameters of image acquisition (orientation of the image, spatial position
of the camera) and the relief (described generally by a DTM, digital terrain
model). It is therefore clear that the precision of the final product depends
directly on the quality of these two data sets.
Let us note here that one knows how to get a DTM currently by automatic
image matching of images. It is more or less today the only operation that
may be completely automated in digital photogrammetry, as the other tools
that tomorrow may be accessible (automatic drawing of roads, extraction of
buildings, etc.) currently require the supervision of a human operator.
The user will sometimes not need a very advanced cartographic quality,
only a fairly constant mean scale, for example within 10 per cent, which
is not compatible with the raw photo but may be performed without
rigorous photogrammetric process. For example, commercial software for
image manipulation (advertisement, editing, retouching of amateur photographs,
etc.) may be used the proper way: one will search for some
identifiable points of known coordinates, and one will distort the image
in order to oblige it to respect their positions. Certainly it is not at all an
orthophotography, but it may provide some facilities and will often be less
expensive. But it is necessary to avoid using the same denomination: one
will speak, for example, of rectified images. The term ‘orthorectified’ image

284 Michel Kasser and Laurent Polidori
or orthophotography would be an abuse here. We will use the generic
term ‘rectified’ image for any image that underwent a process that distorts
it geometrically to bring it closer to an orthophotography. This rectification
can therefore be performed at various levels: so the orthophotography
represents the highest possible level concerning rectification.
Otherwise, most users need numerous images to cover a given area, which
requires a ‘mosaiquage’, meaning that it is necessary to process the links
between images so that one will no longer notice them, in terms of geometry
(breakage in linear elements) and of radiometry as well (differences
of grey level, or of hue, for one given object on two nearby images). For
the geometric aspects, the previous considerations will help to get an idea
of the nature of the problems susceptible of being met. On the other hand,
for radiometric aspects, the physical phenomena originating them are
numerous: chemical process of images, difference of quantity of light
distributed by the same object in different directions (bidirectional reflectance),
images possibly acquired at different dates, or merely at different
instants (and therefore lighting), etc.
Let us add again a few elements of terminology used in the spatial images
process:
• One can say that a image is ‘georeferenced’ if a geometric model is
defined, permitting one to calculate the ground coordinates of every
point of the image. For example, a grid of distortions will be provided
with the image, this remaining raw otherwise.
• An image is said to be ‘geocoded’ if it has been already more or less
rectified (with, in consequence, a better scale constancy).
3.7.3 The market for orthophotography today
One will have understood that all these photographic products have in
common to leave the work of interpretation to the final user. Experience
shows besides that, if most users of geographical information have in
general sometimes important difficulties in reading and exploiting a map,
on the other hand practically everybody will be able, even without any
technical culture, to understand and to interpret the full content of a photographic
document. Multiple cadastral investigation examples in rural Africa
can be found in support of this observation.
This ease of use makes it in fact an excellent support of communication,
or even of negotiation, in particular for decision making related to regional
development (individual citizens, elected people, administrations, etc.).
Otherwise, as mentioned previously, the development of rectified images
is capable of a very high level of automation, which has considerably
decreased the production costs for some years. One even foresees shortly an
entirely automatic production possibility, with very common computers of
PC-type. One will thus have access to a product hardly more expensive than

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the image of origin (this is more or less true as far as the DTM is available),
and that will be able to be practically orthorectified without additional cost.
Besides, it could become of little use to produce badly rectified images.
Let us note again that the recent evolutions of the PC permit comfortable
manipulations of digital images, even the very voluminous and numerous
ones, so that the orthophotography often became the basic layer of urban
GIS, the only one that may be updated regularly.
There are therefore many reasons to anticipate a major development of
the market of the digital orthophotography, and it will not necessarily be
the same for imperfectly rectified images.
Besides, several countries have undertaken or even finished and maintain,
a national coverage in digital orthophotographies.
3.7.4 The different levels of rectification
From the aerial image to orthophotography 285
Given that heterogeneous metric quality products discussed previously
coexist, it appears desirable to clarify concepts of the used terminology.
There are only five applicable quality criteria on the subject, if we look
at the customer’s needs:
1 Geodetic criterion: precision of the correspondence between coordinates
of objects in the official national reference frame and in the
rectified image (if coordinates are displayed in the document): so, if
the system of coordinates is not sufficiently known (for lack of links
to the local geodesy for example), the coordinates that the user can
extract from the image will be in error by a constant value, which can
be very significant. This type of error, for certain applications, has no
importance, but will be bothersome in others (e.g. for somebody
performing further work with GPS).
2 Scale quality criterion: stability of the image scale, or more precisely
evaluation of the scale gap between the image and the corresponding
theoretical map (whose scale is not precisely constant according to the
system of projection used). One can speak of a scale stability within
10 per cent (coarse process), and up to 0.01 per cent (the most precise
processes). This criterion is certainly the most important of all. Let’s
not forget here that the precision of the DTM (a concept otherwise
difficult to define exactly) appears directly in this criterion: if the DTM
is false, the rectification will necessarily be the same!
3 Object scale criterion: in relation with the criterion (5) below, does
the criterion (2) apply only to the ground, or also to objects above
the ground? This point is currently important because the DTM only
concerns the ground, and removes, as much as possible, these objects
(buildings, trees, etc., see §3.3).
4 Radiometric process criterion: concerning the visual quality of the rectified
image, we must note that all resampling will imply a certain

286 Michel Kasser and Laurent Polidori
deterioration of the contour cleanness. The visual quality of the image
assembly includes several more or less appreciable aspects: specular
reflections on water surfaces (whose suppression sometimes implies
heavy manual work), balancing of hues on links (that may require a
human intervention for a good result), etc.
5 Building process criterion: in the case of the urban zones, the presence
of large buildings creates specific difficulties often implying a
manual intervention (digital model of the relief is incomplete because
of zones that are not seen in stereo, hidden zones where images’ sources
do not give any information, etc.). In this criterion, two important
technical aspects are the value of the focal length of the camera used
(the more important it is, the less the image acquired is usable to get
the DTM, so that it will be necessary with the use of a long focal
distance to have the DTM already done elsewhere, but the more the
problems of building facades will be reduced), and the overlap between
the exploited images (if the overlap is very significant, it allows one
to use only the central zones of images, where there are little or even
no problems with buildings).
For these last two aspects, the operator’s interventions can be more important.
The final quality is thus quite difficult to specify, and it implies some
very variable and sometimes major costs.
Finally one will be able to refer also to process specifications in use in
the spatial imagery. Levels of SPOT images processes are typical examples
of what is currently proposed:
• Level 1: raw image.
• Level 2: rectified image with the exclusive use of image acquisition
parameters, but without information on the relief (product being sufficient
in zones of plane for some applications). Such a product will be
accessible when one obtains the digital images with their orientation
and localization parameters.
• Level 3: image rectified by using image acquisition parameters and a
DTM. The result will be therefore an orthophotography.
But currently, no terminology has been dedicated by the use to distinguish
the different qualities of process. It would be most helpful if the rectified
products suppliers systematically provide evaluations on the five criteria
above. For the development of this sector of activities, it is indeed not
desirable that the present confusion persists. For example criteria (2) and
(3), although quite essential, are almost never specified today.
3.7.5 Technical factors seen by the operator
Let us now make a synthesis of elements of the technical process concerning
the operator in the final quality of a rectified image:

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• The DTM can be obtained directly from the exploited stereoscopic
cover and the corresponding stereopreparation. Criteria: precision of
the stereopreparation, quality of the altimetric restitution. If the DTM
is provided by the customer, or obtained in available external databases,
one will observe a separation of responsibilities between the
operator and the supplier of the DTM, which can lead to a complete
removal of responsibility from the operator! Criterion: precision of
altitudes of the DTM.
• Parameters of image acquisition are, in all present processes, unavoidable
by-products of the photogrammetric part of the process
(aerotriangulation). Criterion: are the parameters of image acquisition
used?
• The knowledge of the reference frame is not a simple problem. It even
occurs in certain regions of the world that one doesn’t have access to
it at all. Without reaching this point, there is again there a sharing of
responsibilities between the operator and the supplier of reference
points, capable of removing the responsibility from the operator.
Otherwise, the altimetry being generally referenced on the geoid and
planimetric coordinates being purely geometric (referenced on an ellipsoid),
a large confusion often reigns in altimetric reference systems
used (national levelling network, GPS measures, etc.). Besides, traditional
national planimetric networks have, at the time of a generalized
use of the GPS, important errors often hardly known: one cannot reference
an image rectified in such a system without adjusting the error
model locally, and it implies ground measurements. Criterion: knowledge
of the planimetric and altimetric reference frames.
• The human intervention is more critical to reach the desired quality
(in particular visual): study of reference points, geometric continuity
across the links, radiometric continuity, process of buildings, etc.
Criteria: qualifications, practice and care of the operator.
It is finally necessary to put users on guard against the fact that more and
more commercial software proposes the functionality of geometric distortion
of an image that can look like a rectification of the image. It is due
to the explosion of the market of the digital photograph (warping,
morphing, etc.). As we saw previously, these processes that are completely
unaware of the geometric origin of the treated problem can only provide
some mediocre results. At a time where a rigorous orthorectification is
becoming almost entirely automatic and therefore financially painless, we
can only encourage the users to take care with such products.
3.7.6 Conclusion
From the aerial image to orthophotography 287
The customer sometimes accepts too easily the available product limits for
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288 Michel Kasser and Laurent Polidori
the nomenclature of products and the underlying concepts is absolutely
necessary if one wants to enjoy the expansion of this market, which must
improve on healthier bases. Otherwise a certain ‘democratization’ of
orthorectified images appears indisputable today. If beneficiaries of service
in this matter don’t come from the geomatics technical environment, and
don’t have a sufficient culture concerning geographical information (in
particular concerning photogrammetry), it may be anticipated that the
available products will for a long time present a quality level much lower
than what is possible, this despite the perfectly good faith of the operator,
and for the same price as a rigorous process . . .
3.8 PRODUCTION OF DIGITAL ORTHOPHOTOGRAPHIES
Didier Boldo
3.8.1 Introduction
In theory, a line of orthoimages production can be analysed in very simple
modules. It uses in input the images, the geometry of the image acquisition
and a digital surface model (DSM). From these data one may build
the orthoimages covering the whole zone. One calculates a mosaic, does
a radiometric balancing and then archives the results. (See Figure 3.8.1.)
Images can originate from numerous sources. Generally, one uses very
precisely silver halide scanned images (pixel of 21 to 28 microns). Their
main inconvenience is their lack of radiometric consistency that creates
problems at the time of the orthoimages mosaics calculation. These images
generally have some very important sizes (typically of the order of 300
Mo for colour images), which requires computer power for their manipulation.
If these data are used, the line of production must foresee some
professional scanners, as well as the companion equipment.
But new types of data become available: images originating from digital
cameras, from linear CCD aerial sensors and high-resolution satellite
images. These data have the advantage of an excellent internal radiometric
Images
Geometry of image
acquisition
Digital surface
model
Orthoimages
computation
Mosaic
computation
Figure 3.8.1 Production of digital orthophotographies.
Radiometric
balancing
Archive

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consistency, which greatly simplifies the processes of mosaic calculation.
However, these processes can represent an important part of the calculation
of the orthoimage, notably in terms of operator time.
These images possess a geometry, produced through aero- or spatiotriangulation.
These calculations allow one to determine the direction of
every pixel of each image. These calculations can be integrated in the line
productions. This situation has the advantage of allowing one to use algorithms
in order to automate part of the work, e.g. the detection of link
points (see §2.4).
The last requested data is the digital surface model. In the case of classic
orthoimages, it is a digital terrain model that is generally available on the
shelf as outside data in most western countries. But if one wishes to make
a true orthoimage, it is necessary to use a more precise model. This model
can come from an aerial laser scanner, from automatic correlation, or from
classic photogrammetric restitution. If these models are precise and corrected
enough, they can even permit one to straighten the images of the
buildings.
In fact, the necessary data to manufacture orthoimages can be integrated
in assembly lines of production. So the aspects of calculation of the image
geometry (see §1.1), of calculation of the DSM (see §3.2), and problems
of colour consistency (see §1.3) are integrated generally in the production
chain.
Some automatic tools for the calculation of join-up lines and for balancing
radiometry are now available. They permit important gains of operator
time. Balancing the radiometry of images is a complex problem, difficult
to model, in particular for scanned images (mostly due to the imperfections
of the photographic acquisition, see §1.8). Problems of colour are due to
movements of the sun and variations of the angle optical axis–sun. It generates
problems of hot spot and of specular reflections. One zone has different
aspects therefore according to the chosen image.
3.8.2 Line of join up
Production of digital orthophotographies 289
The automatic calculation of join-up lines on images of good radiometric
quality is a relatively simple problem. Let’s place us in the zone of the
two orthoimages superposition. In this zone, every ground point possesses
two representations: one in each orthoimage. The line of join-up is merely
a path joining two opposite sides of this zone. One wants this line to be
as invisible as possible. For that, one is going to assign a cost value to
every point of the recovery zone. This value represents the ‘visibility’ of a
join-up line if it passes by this point. A measure can be the difference
between the grey level of pixels. Another measure can be the presence of
a contrast between the two images. The line of join-up will then be the
minimum cost path. (See Figure 3.8.2.)

290 Didier Boldo
Figure 3.8.2 Automatic join-up example between four digital images.
3.8.3 Radiometric balancing
As is clearly visible on Figure 3.8.3 (colour section), radiometric differences
between images, especially scanned images, can be very important.
They may have many causes, such as the chemical aspects of the development,
the adjustment of the scanner and the movements of the sun.
Misleading differences between images can be very bothersome. Besides,
these differences can put in failure the algorithm of calculation of join-up
line presented above. For scanned images, the problem of modelling the
difference is very complex, or even impossible. The used methods are therefore
generally empirical. They use parameters that must be adjusted by
hand and require a certain experience.
One of the essential problems is the volume of data. Thus, the regular
cover (every 5 years) of French territory performed by IGN-F by a colour
orthophotography of ground pixel 50 cm represents 1,200 Go of data. It
is necessary to bring in at least as much data for images, then for overlap
zones as well as auxiliary data. It represents 3 Tera-Bytes (4,800 CD-
ROM) of data that must transit production lines and be archived every
year. Material and software solutions exist, but are relatively heavy to
operate. Obviously this part of the problem will progressively disappear
with the evolution of informatics.

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Figure 3.8.3 Scanned images before balancing.
Figure 3.8.4 Scanned images after balancing.
3.8.4 Conclusion
Production of digital orthophotographies 291
Having examined the bases of the orthophotography process, we will see
in the next section (§3.9) how to perform the practical production itself.
An important point must nevertheless be raised now: as mentioned in
§3.7 the production of orthophotographies is quite different if we are in
urban or in rural zones. In rural areas, the main quality aspect will come
from the correct mosaicking (particularly the problem of ‘hot spot’),
nobody will notice the way the trees or the fences are represented. In urban
areas, the representation of the buildings induces another set of difficulties

292 Didier Boldo
already mentioned (hidden zones, very dark shadows, etc.). Thus the software
used for such zones are mostly different. This must be taken into
account when one thinks of a production line.
3.9 PROBLEMS RELATING TO ORTHOPHOTOGRAPHY
PRODUCTION
Didier Moisset
The orthophotography is an artificial digital picture. Completely manufactured
by the computer, it looks automatically in photographs for radiometry
information and borrows from the map, of automatic way, its
carroyage, its bootjacks and sometimes some vector complements (contour
lines, roads, site names, etc.).
It is neither a photo nor a map and the customer wants it to be both
as beautiful as the photo and as precise as the map. This ambiguousness
can cause some problems for the producer of orthophotos. One used to
say that the data size was a major problem. The advent of the fast networks
and very high capacity drives allied to the increasing strength of machines
makes this affirmation less and less true. Since the production is fully
computerized, it is legitimate to want it completely automatic and this is
the case most of the time when the image acquisition is good, the landscape
simple, and the control data of good quality. One will notice that
these conditions are sometimes present (particularly on the data sets that
are used for software demonstrations!), but only ‘sometimes’.
In a situation of mass production, conditions are sometimes very different
and problems occur quickly when, in spite of the power of our machines,
data don’t permit, by their nature, the association of the aesthetic quality
Figure 3.9.1 Example from a real production (digital aerial camera).

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of the photo and the precision of the map. Of course, it is when he counts
in its significant cost that the volume of data manipulated becomes appreciable
for the producer.
The homogeneity of the radiometry
Problems of orthophotography production 293
Let’s imagine an automatic production chain that would only put in
evidence at the time of the mosaicking that the nature of the digital pictures
originating from the scanner do not allow a correct radiometric equating
to be performed. (See Figure 3.9.2, colour section.)
Figure 3.9.2 Example from a real production problem: the radiometric balancing
on digitized pictures.

294 Didier Moisset
This example from a real production is a caricature that shows us the
importance of an efficient procedure of validation of scanning operations
for the production chain. The replacement of a film during the aerial
mission, the modification of chemical film process or a problem in the calibration
of the scanner are many factors that can occur and generate locally
for the mosaic bothersome shortcomings as those noted here.
These problems don’t exist as soon as one uses digital cameras, but let
us keep in mind that when a mission spreads in time, the modification of
the landscape can become appreciable, or even intolerable for the mosaic.
The interpretation of the banking of the raised structures
By its very nature, the orthophoto even when it is of high quality is able
to remind us that it is not a photo and sometimes the choice in the position
of the join-up line has a fundamental importance for the aesthetics
of the mosaic (see Figures 3.9.3 (a) and (b)).
The producer must prevent this kind of fantasy and must use possibilities
of modification of the automatic calculation of the join-up line by
imposing points of passage if its tool possesses this functionality. If it is
not the case, he should modify the join-up line by hand making it follow
the characteristic lines of the landscape.
This example is also caricatural, but one can imagine without difficulty
the problem for the producer of the orthophoto who must define and value
the level of sharpness that he needs to grant for the verification and the
possible modification of join-up lines. It is therefore a costly interactive
phase that is going to condition the quality of the final result.
Stretch of pixels
Another difficulty that one frequently meets on landscapes to strong reliefs:
when the optical ray is tangent to the DTM, a displacement on the DTM
doesn’t generate a displacement on the image. The image will provide the
same radiometry therefore for a succession of pixels of the orthophoto.
One says that the pixel is stretched. (See Figures 3.9.4 and 3.9.5, colour
section.)
In this case, which is not rare, the choice of the image that will provide
the radiometry (therefore the position of the join-up line) is determinant
for the quality of the resulting mosaic.
Difficulties bound to the type of landscape
Some landscapes create some difficult problems to solve. The following
are two examples of landscapes whose aspect changes significantly according
to the point of view from which one looks at it.

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Figures 3.9.3 (a) and (b) Example from a real production (area of Dijon).
A correct line of join-up is not just a question of radiometry,
especially in urban zones.
(a)
(b)

296 Didier Moisset
Figure 3.9.4 Examples from the Ariège, France: problems posed by cliffs.
Figure 3.9.5 Generation of stretched pixels.
Sometimes, the join-up line is difficult to conceal whereas there is no
alternative. It is the case in landscapes of strong reliefs where the aspect
of vegetation is going to depend greatly on the angle from which one looks
at it (see Figure 3.9.6, colour section).
It is also the case with specular reflections well known from picture
processors (Figure 3.9.7, colour section).
DTM

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Figure 3.9.6 Example of radiometric difficulties (Ariège, France).
Figure 3.9.7 Example of typical problems on water surfaces.

298 Didier Moisset
Figure 3.9.8 Two examples from the Isère department, France.
Difficulties bound to the geometry
On the examples shown in Figure 3.9.8 (colour section), the radiometric
homogenization (that is acceptable) is going to overlook for a non-aware
eye a serious defect of geometry. It is clear in this case that the DTM and
the result of the aerotriangulation that have both served to elaborate the
orthophotography are not in agreement.
When this observation is performed only via the examination of the
mosaic (which is the final product) one easily understands the consequences
for the producer who must analyse the whole chain starting with the
control points of the aerotriangulation, as well as the nature of difficulties
that is going to meet the person who must value the amount of work
to perform at this step.
But when all goes well
The examples shown in Figure 3.9.9 (colour section) allow one to conclude
on a positive note. When geometry and radiometry are in harmony, and
in particular when the radiometry is very precise (the case of the digital
cameras acquisitions), it is necessary to make the join-up line visible in
the mosaic to remind one that the orthophotography is not originating
from only one unique photo.
By these examples, one can understand the importance that the producer
of orthophotographies will pay to all operations of validation of the
different steps of the process.
As it uses a set of high technologies ranging from photogrammetry to
the development of digital models of land and digital picture processes,
the rigorous realization of an orthophotography at a time is not a simple
thing, even if it presents the strong interest of being automated.

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Problems of orthophotography production 299
Figure 3.9.9 Two examples, using the digital aerial camera of IGN-F. Due to the
linearity of the CCD, there are only very minor radiometric
differences across the join-up line, which may be chosen without
difficulty.

4 Metrologic applications of
digital photogrammetry
INTRODUCTION
At the end of this book, we have a short presentation of some specific
applications of digital photogrammetry, generally at closer ranges and
without aerial acquisition of the images. Two main domains are presented
here, the architectural applications (§4.1) and the metrologic applications
(§4.2). These two domains have experienced a considerable extension in
recent years, mainly because of the use of digital photogrammetry and the
availability of low-cost digital photogrammetric workstations (DPW).
4.1 ARCHITECTURAL PHOTOGRAMMETRY
Pierre Grussenmeyer, Klaus Hanke, André Streilein
4.1.1 Introduction
Compared with aerial photogrammetry, close-range photogrammetry and
particularly architectural photogrammetry isn’t limited to vertical photographs
with special cameras. The methodology of terrestrial photogrammetry
has changed significantly and various photographic acquisitions are
widely in use.
New technologies and techniques for data acquisition (CCD cameras,
Photo-CD, photoscanners), data processing (computer vision), structuring
and representation (CAD, simulation, animation, visualization) and archiving,
retrieval and analysis (spatial information systems) are leading to novel
systems, processing methods and results.
The purpose of this chapter is to introduce, as part of the International
Committee for Architectural Photogrammetry (CIPA), the profound changes
currently stated.
The improvement of methods for surveying historical monuments and
sites is an important contribution to the recording and perceptual monitoring
of cultural heritage, to the preservation and restoration of any

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valuable architectural or other cultural monument, object or site, as a
support to architectural, archaeological and other art-historical research.
4.1.2 Strategies for image processing
Architectural photogrammetry 301
Close-range photogrammetry is a technique for obtaining geometric information,
e.g. position, size and shape of any object, that was imaged on
photos previously.
To achieve a restitution of a 3D point you need the intersection between
at least two rays (from photo to object point) in space or between one
ray and the surface that includes this point. If more than two rays are
available (the objects shows on three or more photos) a bundle solution
is possible including all available measurements (on photos or even others)
at the same time.
These cases lead to different approaches for the photogrammetric restitution
of an object.
4.1.2.1 Single images
A very common problem is that we know the shape and attitude of an
object’s surface in space (digital surface model) but we are interested in
the details on this surface (patterns, texture, additional points, etc.). In
this case a single image restitution can be appropriate.
With known camera parameters and exterior orientation
In this case the interior orientation of the camera and the camera’s position
and orientation are needed. So the points can be calculated by intersection
of rays from camera to surface with the surface known for its shape and
attitude.
Figure 4.1.1
Camera position

302 Pierre Grussenmeyer et al.
Interior orientation does not mean only the calibrated focal length and
the position of the principal point but also the coefficients of a polynomial
to describe lens distortion (if the photo does not originate from a
metric camera).
If the camera position and orientation is unknown at least three control
points on the object (points with known coordinates) are necessary to
compute the exterior orientation (spatial resection of camera position).
Without knowledge of camera parameters
This is a very frequent problem in architectural photogrammetry. The
shape of the surface is restricted to planes only and a minimum number
of four control points in two dimensions have to be available. The relation
of the object plane to the image plane is described by the projective
equation of two planes:
X a 1 x a 2 y a 3
c 1x c 2y 1 ,
Y b 1x b 2y b 3
c 1x c 2y 1 ,
where X and Y are the coordinates on the object’s plane, x and y the
measured coordinates on the image and a i , b i , c i the eight parameters describing
this projective relation.
The measurement of a minimum of four control points in the single
photo leads to the evaluation of these eight unknowns (a 1, a 2, a 3, . . . , c 2).
As a result, the 2D coordinates of arbitrary points on this surface can
be calculated using those equations. This is also true for digital images of
facades. Digital image processing techniques can apply these equations for
Figure 4.1.2

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Architectural photogrammetry 303
every single pixel and thus produce an orthographic view of the object’s
plane, a so-called orthophoto or orthoimage (see §3.7). (See Figure 4.1.2.)
4.1.2.2 Stereographic processing
If its geometry is completely unknown, a single image restitution of a 3D
object is impossible. In this case the use of at least two images is necessary.
According to the stereographic principle a pair of ‘stereo images’ can
be viewed together, which produces a spatial (stereoscopic) impression of
the object. This effect can be used to achieve a 3D restitution of, for
example, facades. (See Figure 4.1.3.)
Using ‘stereo pairs of images’ arbitrary shapes of a 3D geometry can be
reconstructed as long as the area of interest is shown on both images. The
camera directions should be almost parallel to each other to have a good
stereoscopic viewing.
Metric cameras with well known and calibrated interior orientation and
negligible lens distortion are commonly used in this approach. To guarantee
good results the ratio of stereo base (distance between camera
positions) to the camera distance to the object should lie between 1:5 and
1:15.
Results of stereographic restitution can be:
• 2D-plans of single facades;
• 3D-wireframe and surface models;
• lists of coordinates;
• eventually complemented by their topology (lines, surfaces, etc.).
Object distance
Figure 4.1.3
Stereo base

304 Pierre Grussenmeyer et al.
Figure 4.1.4 Stereopair from CIPA-Testfield ‘Otto Wagner Pavillion Karlsplatz,
Vienna’.
Figure 4.1.5 2D façade plan derived from above stereo pair of images.
4.1.2.3 Bundle restitution
In many cases the use of one single stereo pair will not suffice to reconstruct
a complex building. Therefore a larger number of photos will be
used to cover an object as a whole. To achieve a homogeneous solution
for the entire building and also to contribute additional measurements, a
simultaneous solution of all the photo’s orientation is necessary.
Another advantage is the possibility to perform an on-the-job calibration
of the camera. This helps to increase the accuracy when using images
of an unknown or uncalibrated camera. So this approach is no longer
restricted to metric or even calibrated cameras, which makes the applica-

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Architectural photogrammetry 305
Bundle
3 Convergent bundle
1 2 3 4
Figure 4.1.6 Examples of different configurations for bundle solution.
tion of photogrammetric techniques much more flexible. It is also adjustable
concerning the geometry of camera positions, meaning one is not
forced to look for parallel views and stereo pair configuration. Convergent,
horizontally, vertically or obliquely photos are now certainly suitable. Combination
of different cameras or lenses can easily be done.
The strategy of taking photos is that each point to be determined should
be intersected by at least two rays of satisfactory intersection angle. This
angle depends only upon the accuracy requirements. Additional knowledge
of, for example, parallelism of lines, flatness of surfaces and rectangularity
of features in space can be introduced in this process and helps to build
a robust and homogeneous solution for the geometry of the object.
The entire number of measurements and the full range of unknown parameters
are computed within a statistical least squares adjustment. Due to
the high redundancy of such a system it is also possible to detect blunders
and gross errors, so not only accuracy but also reliability of the result
will usually be increased.
Bundle adjustment is a widespread technique in the digital architectural
photogrammetry of today. It combines the application of semi-metric
or even non-metric (amateur) cameras, convergent photos and flexible
measurements in a common computer environment. Because of the adjustment
process, the results are more reliable and accurate and very often
readily prepared for further use in CAD environments.
Results of bundle restitution are usually 3D-wireframe and surface
models of the object or lists of coordinates of the measured points and their
topology (lines, surfaces, etc.) for use in CAD and information systems.
Visualizations and animations or so-called ‘photo-models’ (textured 3Dmodels)
are also common results. Usually the entire object is reconstructed
in one step and the texture for the surface is available from original photos
(see §4.1.6).
5
7
6

Figure 4.1.7 Examples of different images, different cameras, different lenses (from project Ottoburg, Innsbruck) to combine
within a bundle solution (Hanke and Ebrahim, 1999).

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4.1.3 Image acquisition systems
Architectural photogrammetry 307
Figure 4.1.8 Wireframe model and surface model as results of bundle restitution.
4.1.3.1 General remarks
Digital image data may be acquired directly by a digital sensor, such as a
CCD array camera (see §1.5), for architectural photogrammetric work.
Alternatively, it may be acquired originally from a photograph and then
scanned (see §1.8).
For the applications in architectural photogrammetry the use of cameras
was for a long time determined by the use of expensive and specialized
equipment (i.e. metric cameras). Depending on the restrictions due to the
photogrammetric reconstruction process in former times, only metric
cameras with known and constant parameters of interior orientation could
be used. Their images had to fulfil special cases for the image acquisition
(e.g. stereo normal case).
Nowadays more and more image acquisition systems based on digital
sensors are developed and available at reasonable prices on the market.
The main advantage of these camera systems is the possibility to acquire
digital images and directly process them on a computer.
Figure 4.1.9 gives a principal overview of the basic photogrammetric
systems for image acquisition and image processing in architectural photogrammetry.
The classic, photographic cameras have their advantages in
the unsurpassed quality of the film material and resolution and in the wellknown
acquisition technique. The process of analytical photogrammetry
makes a benefit of the knowledge and rich experiences of the human operator.
On the other hand the pure digital data flow has not yet image

308 Pierre Grussenmeyer et al.
Film-based
camera
Film
development
Analogue/Analytical
Photogrammetry
Scanning /
Digitisation
Digital camera
Digital
Photogrammetry
Figure 4.1.9 Image acquisition and image processing systems in architectural
photogrammetry.
acquisition devices comparable to film-based cameras. But this procedure
allows a productive processing of the data due to the potential of automation
and the simultaneous use of images and graphics. Furthermore, it
allows a closed and therefore fast and consistent flow of data from the
image acquisition to the presentation of the results. In addition, with
the digitization of film a solution is available that allows the benefits
of the high-resolution film to be merged with the benefits of the digital
image processing. But the additional use of time for the separate process
of digitization and the loss of quality during the scanning process are disadvantages.
In the following sections the main photographic and digital image
acquisition systems used in architectural photogrammetry are explained,
examples are shown and criteria for their use are given.
4.1.3.2 Photographic cameras
From a photogrammetric point of view, film-based cameras can be subdivided
into three main categories: metric cameras, stereo cameras and
semi-metric cameras (see Table 4.1.1).
Terrestrial metric cameras are characterized by a consequent opticalmechanical
realization of the interior orientation, which is stable over a
longer period. The image coordinate system is, like in aerial metric cameras,
realized by fiducial marks. In architectural photogrammetry such cameras

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Architectural photogrammetry 309
Table 4.1.1 Examples from the variety of film-based image acquisition systems
Manufacturer Type Image format Lenses
[mm 2 ] [mm]
Metric cameras
Hasselblad MK70 60 × 60 60, 100
Wild P32 65 × 90 64
Wild P31 100 × 130 45, 100, 200
Zeiss UMK 1318 130 × 180 64, 100, 200, 300
Stereo cameras
Wild C 40/120 65 × 90 64
Zeiss SMK 40/120 90 × 120 60
Semi-metric cameras
Rollei 3003 24 × 36 15–1000
Leica R5 24 × 36 18–135
Rollei 6006 60 × 60 40–350
Hasselblad IDAC 55 × 55 38, 60, 100
Pentax PAMS 645 40 × 50 35–200
Linhof Metrica 45 105 × 127 90, 150
Rollei R_metrica 102 × 126 75, 150
Rollei LFC 230 × 230 165, 210, 300
Geodetic Services CRC-1 230 × 230 120, 240, 450
are less and less used. Amongst those cameras, which are still in practical
use, are, for example, the metric cameras Wild P31, P32 and Zeiss UMK
1318. Such image acquisition systems ensure a high optical and geometrical
quality, but are also associated with high prices for the cameras
themselves. In addition they are quite demanding regarding the practical
handling. Besides the single metric cameras in heritage documentation,
often stereo cameras are used. These cameras are composed of two calibrated
metric cameras, which are mounted on a fixed basis in standard
normal case. A detailed overview of terrestrial metric cameras can be found
in many photogrammetric textbooks (e.g. Kraus, 1993).
With the use of semi-metric cameras the employment of réseau techniques
in photographic cameras was established in the everyday work of
architectural photogrammetry. The réseau, a grid of calibrated reference
marks projected on to the film at exposure, allows the mathematical
compensation of film deformations, which occur during the process of
image acquisition, developing and processing. Different manufacturers
offer semi-metric cameras at very different film formats. Based on small
and medium format SLR-cameras, systems exists from, for example, Rollei,
Leica and Hasselblad. Their professional handling and the wide variety
of lenses and accessories allow a fast and economic working on the
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310 Pierre Grussenmeyer et al.
between a large-image format and established camera technique. An
overview on semi-metric cameras is given in Wester-Ebbinghaus (1989).
Often in architectural applications so called amateur cameras are used.
This is not for dedicated photogrammetric projects, but in emergency cases,
where no other recording medium was available or in case of destroyed
or damaged buildings when only such imagery is available. Examples are
given in, amongst others, Gruen (1976), Dallas et al. (1995) and Ioannidis
et al. (1996). Due to the ongoing destruction of the world cultural heritage
it will also be necessary in the future to reconstruct objects taken with
amateur cameras (Waldheusl and Brunner, 1988).
4.1.3.3 Scanners
The digitization of photographic images offers a means to combine the
advantages of film-based image acquisition (large image format, geometric
and radiometric quality, established camera technique) with the advantages
of digital image processing (archiving, semi-automatic and automatic
measurement techniques, combination of raster and vector data).
Scanners for the digitization of film material can be distinguished
regarding different criteria. For example, regarding the type of sensor,
either point, line or area sensor, or regarding the arrangement with respect
to the scanned object as flatbed or drum scanner (see §1.8).
For the practical use of scanners in architectural photogrammetric applications
the problem of necessary and adequate scan resolution has to be
faced. On the one hand the recognition of details has to be ensured and
on the other hand the storage medium is not unlimited. This holds especially
for larger projects. To scan a photographic film with a resolution
equivalent to the film a scan resolution of about 12 m (2,100 dpi) is
required. Thus, a scanned image from a medium format film (6 × 6 cm2 )
has about 5,000 × 5,000 pixels. To hold this data on disk requires approximately
25 Mbytes for a black-and-white scan and 75 Mbytes for a coloured
image. For a scanned colour aerial image one would get a digital image
of 20,000 × 20,000 pixels or 1.2 Gbytes. Even with the constant increasing
size and decreasing costs for computer storage medium, this is a not to
underestimate this factor in the planning of a project.
For the use in architectural photogrammetry typically two different types
of scanners are used, high-resolution photogrammetric scanners and
desktop publishing scanners.
The photogrammetric scanners are typically flatbed scanners, which have
a high geometric resolution (5–12.5 m) and a high geometric accuracy
(2–5 m). Currently there are just a few systems commercially available,
which are offered mainly by photogrammetric companies. An overview on
existing systems is given in Baltsavias and Bill (1994).
The desktop publishing scanners (DTP) are not developed for photogrammetric
use, but they are widely available on the market at low cost and

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Architectural photogrammetry 311
they are developed and improved in a short time interval. DTP scanners
have typically a scan size capability of A4 or A3 formats with a scan resolution
of 300–1,200 dpi. The geometric resolution of these systems is about
50 m. Despite this technical reduction compared to photogrammetric
scanners, these scanners, which are low cost and easy to handle, can be
used for photogrammetric purposes. This holds especially for calibrated
systems, where geometric accuracy in the order of 5–10 m is feasible
(Baltsavias and Waegli, 1996).
Another possibility for the digitization and storage of film material is
offered by the Photo-CD system. Small and medium format film can be
digitized in a special laboratory and stored on CD-ROM. The advantage
of such a system is the inexpensive and easy digitization and convenient
data archiving. On the other hand the scanning process cannot be controlled
or influenced and the image corners are usually not scanned. Thus
the interior orientation of an image is nearly impossible to reconstruct.
Investigations about the practical use of the Photo-CD system for digital
photogrammetry are performed by Hanke (1994) and Thomas et al.
(1995).
4.1.3.4 CCD cameras
The development of digital image acquisition systems is closely connected
to the development of CCD sensors. The direct acquisition of digital images
with a CCD sensor holds a number of advantages, which makes them
interesting for photogrammetric applications. For example:
• direct data flow with the potential of online processing;
• high potential for automation;
• good geometric characteristics;
• independent of the film development process;
• direct quality control of the acquired images;
• low-cost system components.
For photogrammetric applications mainly area-based CCD sensors are
used. These sensors are produced for the commercial or industrial video
market. Area-based CCD sensors are used in video cameras as well as in
high resolution digital cameras for single exposures (still video cameras).
Furthermore, there are specialized systems that use a scanning process for
the image acquisition.
Standard CCD video cameras have a number of 400–580 × 500–800
sensor elements. With a pixel size of 7–20 m these cameras have an
image format between 4.4 × 6.0 mm and 6.6 × 8.8 mm. Such cameras
deliver a standardized, analogue video signal with 25–30 images per second.
This signal can be displayed on any video monitor. For the photogrammetric
processing of this signal, it has to be digitized by a frame grabber.

312 Pierre Grussenmeyer et al.
Beside the entertainment industry such video cameras are mainly used for
simple measurement or supervision tasks. The variety of systems on the
market is enormous and can hardly be followed. Such systems are of importance
for the documentation of destroyed objects of the world cultural
heritage. Under certain circumstances the reconstruction of a building from
video imagery is possible (Streilein, 1995).
One of the newer developments of digital image acquisition devices are
CCD video cameras with a digital output. These cameras offer an A/D
conversion in the camera body and have storage capacity for one acquisition,
so that it is possible to store the image. The digital image can be
delivered to a computer, the transfer of the image data is practically free
of noise.
Due to the restrictions regarding resolution of CCD video cameras
and due to the ongoing improvements in the CCD market, today more
and more high-resolution digital cameras are used. Such cameras can be
described as a combination of a traditional small-format SLR camera with
a high-resolution CCD sensor replacing the film. The digital image data
is stored directly in the camera body. In the photogrammetric community
very well-known representatives of this type of camera are distributed from
Kodak/Nikon under the Name DCS 420 and 460. They offer resolutions
of 1,524 × 1,012 pixel and 3,060 × 2,036 pixel respectively. In addition,
various manufacturers (e.g. Kodak, Leaf, and Rollei) offer camera systems
with a resolution of about 2,000 × 2,000 pixels. The main advantage of
such systems is the fast and easy image acquisition. This is achieved due
to the fact that image acquisition, A/D conversion, storage medium and
power supply are combined in one camera body. This allows one to transfer
the images immediately to a computer and to judge the quality of the
acquired images or directly process them.
Scanning cameras improve the resolution of the final image by sequential
scanning procedure. Two scanning principles are distinguished, micro
scanning and macro scanning (Lenz and Lenz, 1993). Micro scanning
cameras use the principle of moving a CCD area sensor in parts of the
pixel size over the sensor. The final image will be calculated from the
different single images taken after the movement. The format of the final
image is the same as that of the single images. The resolution of the final
image is increased in horizontal and vertical directions by the number of
the single images taken in each direction (microscan factor). Macro scanning
cameras on the other hand move a CCD area sensor over a large
image format. The position of the single images taken is determined either
optical-numerically or mechanically, such that the single images can be
combined into one high-resolution image. Both methods have in common
that they should be used when object and camera do not move during the
period of image acquisition (typically several seconds). Furthermore, the
illumination conditions should remain constant during that period. This
is practically achievable only under laboratory conditions, so that such

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Architectural photogrammetry 313
Table 4.1.2 Examples from the spectrum of digital image acquisition devices
Manufacturer Type Number of pixel Image format
(HV) [mm 2 ]
Pulnix TM-560 582 × 500 8.8 × 6.6
Canon ION RC 560 795 × 576 8.8 × 6.6
Sony XC-77 768 × 593 8.8 × 6.6
JVC GRE-77 728 × 568 6.4 × 4.8
Canon EOS-DCS 3 1268 × 1012 20.5 × 16.5
Kodak Megaplus-1.4 1320 × 1035 9.0 × 7.0
Agfa ActionCam 1528 × 1148 16.5 × 12.4
Kodak DCS 420 1524 × 1012 14.0 × 9.0
Kodak Megaplus-4.2 2048 × 2048 18.4 × 18.4
Rollei ChipPack 2048 × 2048 31.0 × 31.0
Kontron ProgRes 3000 2994 × 2320 8.6 × 6.5
Kodak DCS 460 3060 × 2036 30.0 × 20.0
Canon EOS-DCS 1 3060 × 2036 27.6 × 18.4
Dicomed BigShot 4096 × 4096 60.0 × 60.0
Kodak Megaplus-16.8 4096 × 4096 36.8 × 36.8
Agfa StudioCam 4500 × 3648 36.0 × 29.0
RJM JenScan 4500 × 3400 8.8 × 6.6
Jenoptik Eyelike 6144 × 6144 28.6 × 28.6
Rollei RSC 7000 × 5500 55.0 × 55.0
Zeiss UMK HighScan 15414 × 11040 166.0 × 120.0
systems have minor importance for applications in architectural photogrammetry.
For applications in architectural photogrammetry line-based sensors can
also be used for the generation of high-resolution images. An example of
this type of sensor used for architectural photogrammetry is given in Reulke
and Scheele (1997). In this example several buildings are recorded using
the WAOSS/WAAC CCD line scanner, which incorporates three line
sensors of 5,184 pixels each.
In Table 4.1.2 a few examples from the great variety of digital image
acquisition systems on the market, which are suitable for applications
in digital architectural photogrammetry, are given. This compilation is
naturally incomplete and is just mentioned to give an idea about the
variety. A good overview on digital image acquisition systems is nowadays
available on different Internet pages, e.g. Plug-In Systems (2000),
PCWebopaedia (2000), or the Internet pages of the different manufacturers.
4.1.3.5 Which camera to use?
For the question which camera to use for a specific photogrammetric task
for heritage documentation, there is basically no common answer or simple
rule. Often a photogrammetric project is as complex as the object itself

314 Pierre Grussenmeyer et al.
and more often the use of an image acquisition device is determined by
the budget of the project (read: use a camera system that is already available
at no cost).
However, for a successful photogrammetric project several aspects have
to be taken into account. For example, the maximum time limit for the
image acquisition on the spot and for the (photogrammetric) processing
of the data afterwards. Further criteria can be: the need for colour images
or black-and-white images, the requested accuracy of the final model, the
smallest object detail that can be modelled, the minimum and maximum
of images for the project, the mobility and flexibility of the image acquisition
system or the integration into the entire production process. But
after all the price of the image acquisition system and the possibilities
for further processing of the image data remain as the major factors for
selecting a specific image acquisition system for a specific project.
4.1.4 Overview of existing methods and systems for
architectural photogrammetry
4.1.4.1 General remarks
Architectural photogrammetry and aerial photogrammetry don’t have the
same applications and requirements. Most of the commercial digital
photogrammetric workstations (DPWs) are mainly dedicated to stereoscopic
image measurement, aerial triangulation, the digital terrain model
(DTM) and orthoimages production from aerial and vertical stereopair
images. A survey of these DPWs is presented by Plugers (1999). In this
section we consider systems and methods which are rather low cost
comparing to those well-known products developed mainly for digital
mapping. Software packages for architectural photogrammetry may use
different image types, obtained directly by CCD cameras or by scanning
small and medium format metric or non-metric slides (see §4.1.3). The
quality of digital images directly influences the final result: the use of lowresolution
digital cameras or low-priced scanners may be sufficient for
digital 3D visual models but not for a metric documentation. The systems
may be used by photogrammetrists as well as by architects or other specialists
in historic monument conservation, and run on simple PC-systems that
suffice for special tasks in architectural photogrammetry.
According to the specific needs in architectural documentation, the
different kinds of systems are based either on digital image rectification,
or on monoscopic multi-image measurement or on stereoscopic image
measurement (Fellbaum, 1992). Software of such systems is advanced in
such a way that mass restitution and modelling is possible, if digital images
are provided in a well-arranged way. Only some software packages are
mentioned in this paragraph, and the aim is not to make a survey of
existing systems.

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To compare different systems, the following topics can be considered
(CIPA, 1999):
• the handling of a system;
• the flow of data;
• the management of the project;
• the import and export of data (image formats, parameter of interior
and exterior orientation, control information, CAD information);
• the interior orientation;
• the exterior orientation (one step or two steps);
• the reconstruction of the object;
• the derived results in terms of topology, consistency, accuracy and reliability;
• the amount of photogrammetric knowledge necessary to handle the
system.
4.1.4.2 Recommendation for simple photogrammetric
architectural survey
For simple photogrammetric documentation of architecture, simple rules
that are to be observed for photography with non-metric cameras have
been written, tested and published by Waldheusl and Ogleby (1994).
These so-called ‘3 × 3 rules’ are structured in:
1 three geometrical rules:
i preparation of control information;
ii multiple photographic all-around coverage;
iii taking stereopartners for stereo-restitution.
Architectural photogrammetry 315
Figure 4.1.10 Ground plan of a stable bundle block arrangement all around
building, as recommended in the 3 × 3 rules
[see http://www.cipa.uibk.ac.at].

316 Pierre Grussenmeyer et al.
2 three photographic rules:
i the inner geometry of the camera has to be kept constant;
ii select homogeneous illumination;
iii select most stable and largest format camera available.
3 three organizational rules:
i make proper sketches;
ii write proper protocols;
iii don’t forget the final check.
Usually, metric cameras are placed on a tripod, but shots with small or
medium format equipment are often taken ‘by hand’. Recently, digital
phototheodolites combining total-station and digital cameras have been
developed by Agnard et al. (1998), and Kasser (1998). Digital images are
then referenced from object points or targets placed in the field. In this
way, the determination of the exterior orientation is simple and the images
are directly usable for restitution.
4.1.4.3 Digital image rectification
Many parts of architectural objects can be considered as plane. In this
case, even if the photo is tilted with regard to the considered plane of the
object, a unique perspective is enough to compute a rectified scaled image.
We need at least four control points defined by their coordinates or
distances in the object plane (§2.3.2).
The Rolleimetric MSR software package [http://www.rolleimetric.de]
provides scale representations of existing objects on the basis of rectified
digital images (Figures 4.1.11 (a), (b) and (c)). The base data is usually
one or more photogrammetric images and/or amateur photographs of the
object that are rectified at any planes defined by the user. Simple drawings
(in vector-mode), image plans (in raster-mode) are processed as a
result of the rectification.
Basically, the major stages encountered in the rectification of photography
are as follows (Bryan et al., 1999):
• site work (photography and control);
• scanning;
• rectification;
• mosaicking;
• retouching;
• output;
• archive storage.
Photographs of building façades should be taken the most perpendicular
to the reference planes and only the central part of the image should
be considered for a better accuracy.

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(a)
(b)
Architectural photogrammetry 317
Figure 4.1.11 (a) Selection of a ‘plane’ part of the object. (b) Control distances
for the plane definition. (c) Rectified image as an extract of (a).
Commercial CAD/CAM software packages often include image handling
tools and also allow simple image transformation and rectification. But
they seldom consider camera distortions, as opposed to photogrammetric
software.
In the case of a perspective rectification, radial image displacements in
the computed image will occur for points outside the reference. The rectification
obviously fails if the object isn’t somewhat plane.
Some packages include functions for the photogrammetric determination
of planes according to the multi-image process (§4.1.4.4) from two
or three photographs that capture an object range from different viewpoints.
Digital image maps can be produced by assuming the object surface
and photo rectification. In the resulting orthophoto, the object model is
represented by a digital terrain model (Pomaska, 1998). Image data of
different planes can be combined into digital 3D computer models for visualization
and animation with the help of photo editing or CAD software.
ELSP from PMS [http://www.pms.co.at] and Photoplan [http://www.
photoplan.net] are other examples of commercial systems particularly dedicated
to rectification.
Besides digital image rectification and orthoimaging, single images for
3D surfaces of known analytical expression may lead to products in raster
form, based on cartographic projections. Raster projections and developments
of non-metric imagery of paintings on cylindrical arches of varying
diameters and spherical surfaces are presented in Karras et al. (1997) and
Egels (1998).
4.1.4.4 Monoscopic multi-image measurement systems
Photogrammetric multi-image systems are designed to handle two or more
overlapping photographs taken from different angles of an object (see
§4.1.2.3). In the past, these systems were used with analogue images
(c)

318 Pierre Grussenmeyer et al.
enlarged and placed on digitizing tablets. Presently, the software usually
processes image data from digital and analogue imaging sources (réseau,
semi-metric or non-metric cameras). Scanners are used to digitize the
analogue pictures. Film and lens distorsions are required to perform metric
documentation. Monoscopic measurements are achieved separately on each
image. These systems don’t give the opportunity of conventional stereophotogrammetry.
For the point measurements and acquisition of the object
geometry, systems can propose support:
• for the automatic réseau cross-measurement;
• for the measurement of homologous points through the representation
of line information in the photogrammetric images and epipolar
geometry.
The acquisition of linear objects can be directly evaluated due to superimposition
in the current photogrammetric image. These systems are
designed for multi-image bundle triangulation (including generally simultaneous
bundle adjustment with self-calibration of the used cameras, see
§2.3). The main differences between the systems consist in the capabilities
of the calculation module to combine additional parameters and
knowledge, like directions, distances and surfaces. The main contribution
of digital images in architectural photogrammetry is the handling of
textures. The raster files are transformed into object surfaces and digital
image data is projected on to a three-dimensional object model. Some
systems are combined with a module of digital orthorectification.
The Canadian Photomodeler Software Package developed by Eos Systems
is well known as a low-cost 3D-measurement tool for architectural and
archeological applications [http://www.photomodeler.com]. Photomodeler
(Figure 4.1.12) is a Windows-based software that allows measurements
and transforms photographs into 3D models. The basic steps in a project
performed with Photomodeler are:
• shoot two or more overlapping photographs from different angles of
an object;
• scan the images into digital form and load them into Photomodeler;
• using the point and line tools, mark on the photographs the features
you want in the final 3D model;
• reference the points by indicating which points on different photographs
represent the same location on the object;
• process referenced data (and possibly the camera) to produce 3D
model;
• view the resulting 3D model in the 3D viewer;
• extract coordinates, distances and areas measurements within Photomodeler;
• export the 3D model to rendering, animation or CAD program.

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Architectural photogrammetry 319
Figure 4.1.12 Photomodeler’s measuring module (project ‘Ottoburg, Innsbruck’,
see §4.1.6).
Fast camera calibration based on a printable plane pattern can be set up
separately to compute the camera’s focal length, principal point, digitizing
aspect ratio and lens distortion. Images from standard 35 mm film cameras
digitized with Kodak Photo-CD, negative scanner or flatbed scanner as
well as from digital and video cameras can be used in Photomodeler. The
achieved accuracy obtained by Hanke and Ebrahim (1997) for distances
between points lies in the range of 1:1,700 (for a 35 mm small format
‘amateur’ camera, without lens distortion compensation) to 1:8,000 (for
a Wild P32 metric camera) and shows promising results.
Examples of systems based on the same concept are:
• KODAK Digital Science Dimension Software [http://www.kodak.com],
with single and multiple image capabilities.
• 3D BUILDER PRO [http://aay.com/release.htm], with a ‘constraintbased’
modelling software package.
• SHAPECAPTURE [http://www.shapequest.com] offers target and
feature extraction, target and feature 3D coordinate measurement, full
camera calibration, stereo matching and 3D modelling.
• CANOMA [http://www.metacreations.com] from Meta Creations is a
software intended for creating photorealistic 3D models from illustrations
(historical materials, artwork, hand-drawn sketches, etc.),
scanned or digital photographs. Based on an image-assisted technique,
it enables one to attach 3D wireframe primitives and to render a 3D
image by wrapping the 2D surfaces around these primitives.

320 Pierre Grussenmeyer et al.
Some other systems, also based on monoscopic multi-image measurement,
are not mainly dedicated to the production of photomodels. In
general, they use CAD models for the representation of the photogrammetric-generated
results. For examples there are:
• CDW from Rolleimetric [http://www.rolleimetric.de] which is mainly
a measuring system and doesn’t handle textures. Data are exported to
the user’s CAAD system by interfaces. MSR 3D , also proposed by Rolleimetric,
is an extension of MSR and is based on a CDW multi-image
process (two or three photographs) for the determination of the different
object-planes and the corresponding rectified images.
• Elcovision12 from PMS [http://www.pms.co.at] can run standalone or
be directly interfaced with any CAAD application.
• PICTRAN from Technet (Berlin, Germany) [www.technet-gmbh.com]
which includes bundle block adjustment and 3D restitution as well as
rectification and digital orthophoto.
• PHIDIAS, proposed by PHOCAD (Aachen, Germany) is integrated in
the Microstation CAD package.
• ORPHEUS (ORIENT-Photogrammetry Engineering Utilities System),
proposed by the Institute of Photogrammetry and Remote Sensing of
the Vienna University of Technology (Austria), is a digital measurement
module running with the ORIENT software, linked with the
SCOP software for the generation of digital orthophotos. It allows
one, more particularly, to handle large images by the creation of image
pyramids.
The prototype DIPAD (digital system for photogrammetry and architectural
design) is based on the idea of using CAD models in a priori and
a posteriori modes. Therefore CAD models are not only used for the
graphical visualization of the derived results, but a complete integration
between CAAD environment and photogrammetric measurement routines
is realized. No manual measurements have to be performed during the whole
analysis process. The system allows the three-dimensional reconstruction of
objects or parts of it as an object-oriented approach in a CAAD-controlled
environment. The task of object recognition and measurement is solved,
with the image interpretation task performed by a human operator and the
CAD-driven automatic measurement technique derives the precise geometry
of the object from an arbitrary number of images. A human being uses
intuitively, while looking at an image, his/her entire knowledge of the real
world and is therefore able to select the information from or add missing
information to the scene, which is necessary to solve the specific task.
By choosing a combined top-down and bottom-up approach in feature
extraction, a coarsely given CAD model of the object is iteratively refined
until finally a detailed object description is generated. The semi-automatic
HICOM method (human for interpretation and computer for measurement)

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is able to simplify the analysis process in architectural photogrammetry
without degradation in accuracy and reliability of the derived results.
Typical problems for the automatic analysis of image data, which are very
common in outdoor scenes, like occlusions of the object by itself or due to
other objects (e.g. persons, vegetation), shadow edges and reflections, are
detected with this method and attributed during further processing.
Examples for the performance of this method are given in, for example,
Streilein (1996) and (Streilein and Niederöst, 1998).
4.1.4.5 Stereoscopic image measurement systems
Architectural photogrammetry 321
Figure 4.1.13 Screenshot of DIPA during the reconstruction process (interaction
takes only place in the lower left CAD environment).
From analytical to digital
Digital stereoscopic measuring systems follow analytical stereoplotters well
known as the more expensive systems. Many plottings are still done on
analytical stereoplotters for metric documentation but as the performance
and ability of digital systems increase and allow mass restitution. As
textures are increasingly required for 3D models, digital photographs and
systems are getting more and more important.

322 Pierre Grussenmeyer et al.
Stereoscopy
Systems presented in the former paragraph allow more than two images
but homologous points are measured in monoscopic mode. Problems
may occur for objects with less texture when no target is used to identify
homologous points. Only stereo-viewing allows in this case a precise
3D measurement. Therefore stereopairs of images (close to the normal
case) are required. Systems can then be assimilated to 3D plotters for the
measuring of spatial object coordinates. 3D measurements are required for
the definition of digital surface models that are the basis of the orthophotos.
Usually, proposed solutions for stereo-viewing devices are:
• the split-screen configuration using a mirror stereoscope placed in front
of the screen;
• the anaglyph process;
• the alternating of the two images on the full screen (which requires
active glasses);
• the alternating generation of the two synchronized images on a polarized
screen (which requires polarized spectacles).
Automation and correlation
In digital photogrammetry, most of the measurements can be done automatically
by correlation. The task is then to find the position of a geometric
figure (called the reference matrix) in a digital image. If the approximate
position of the measured point is known in the image, then we can define
a so-called search matrix. Correlation computations are used to determine
the required position in the digital image. By correlation in the subpixel
range the accuracy of positioning is roughly one order of magnitude better
than the pixel size. Usually, the correlation process is very efficient on
architectural objects, due to textured objects. Correlation functions can be
implemented in the different steps of the orientation:
• fiducial marks or réseau crosses can be measured automatically in the
inner orientation;
• measurement of homologous points can be automated by the use of
the correlation process both in the exterior orientation, and in the
digital surface model and stereoplotting modules.
The correlation function is a real step forward compared to manual
measurements applied in analytical photogrammetry. The quality of the
measurement is usually given by a correlation factor.

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Architectural photogrammetry 323
Model orientation
Systems currently used for aerial photogrammetry run with stereopairs of
images but their use isn’t always possible in architectural photogrammetry.
In many cases, systems cannot handle different types and scales of images.
The orientation module may fail either because photographs and control
points are defined in a terrestrial case, or due to the non-respect of the
approximate normal case. For the exterior orientation, some systems
propose solutions based on typical two-step orientation (relative and
absolute), as known in analytical photogrammetry. But bundle adjustment
is increasingly proposed and allows an orientation in only one step. A direct
linear transformation is sometimes used to compute approximate parameters
of the orientation. Some systems propose automatic triangulation.
But due to the configuration of the set of photographs in architectural
photogrammetry, their use requires many manual measurements. After
the relative orientation, often normalized images can be computed. Either
original or normalized images can be used for further processes.
Stereo-digitizing and data collection
3D vectorization allows plottings (Figure 4.1.14) and digital surface model
generation, with more or less semi-automatic procedures depending on the
systems. Image superimposition is possible with almost every DPW. Some
Figure 4.1.14 Digital stereoplotting with image superimposition.

324 Pierre Grussenmeyer et al.
systems can be connected on-line to commercial CAD software packages
and use their modelling procedures. Orthophotos can be generated from
the different models but for architectural application, photomodels are
usually carried out with multi-image systems (see Figures 4.1.6 and 4.1.7).
Examples of low-cost PC-systems based on stereoscopic measurements
with known applications in close-range architectural photogrammetry, but
only handling nearly normal case stereopairs, are:
• The digital video plotter (DVP) [http://www.dvp-gs.com]. It was one
of the first systems proposed (Agnard et al., 1988). It is optimized for
large-scale mapping in urban areas but architectural projects have been
presented by DVP Geomatic Systems Inc.
• Photomod from Raccurs (Moscow, Russia) has a high degree of automatization,
compared to other systems. The system is known as DPW
for aerial photogrammetry. Orthophotos of facades with Photomod
have been presented by Continental Hightech Services [http://www.chscarto.fr].
• Imagestation SSK stereo Softcopy Kit from Intergraph Corporation is
proposed as a kit to convert a PC into a low-cost DPW. Different
modules of Intergraph ImageStation are available.
Several systems have been developed by universities during recent years.
Some of them are:
• VSD as video stereo digitizer (Jachimski, 1995) is well known for
architectural applications; VSD is a digital autograph built on the basis
of a PC. It is suitable for plotting vector maps on the basis of pairs
of monochrome or colour digital images as well as for vectorization
of orthophotographs. The stereoscopic observation is based on a simple
mirror stereoscope.
• POIVILLIERS ‘E’ developed by Yves Egels (IGN-ENSG, Paris, France)
runs under DOS. Stereo-viewing is possible by active glasses connected
to the parallel port of the PC or by anaglyphs. The system is very efficient
for large images and high pointing accuracy is available due to
a sub-pixel measuring module. Colour superimposition of plottings is
also proposed. The system runs on aerial images as well as on terrestrial
ones.
• Mapping from stereopairs within Autocad R14 is proposed by Greek
Universities (Glykos et al., 1999).
• TIPHON is a Windows application developed at ENSAIS (Polytechnicum
of Strasbourg, France) for two-image based photogrammetry
(stereopair or convergent bundle) with different kinds of cameras
(Grussenmeyer and Koehl, 1998). The measurements on the images
are manual or semi-automatic by correlation. A stereoscope is used if
stereoscopic observations are required.

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• ARPENTEUR as ‘ARchitectural PhotogrammEtry Network Tool for
EdUcation and Research’ is a platform-independent system available
on the web by a simple internet browser (Drap and Grussenmeyer,
2000). The system is an adaptation of TIPHON to the Internet World
and is particularly dedicated to architectural applications. ARPEN-
TEUR is a web-based software package utilizing HTTP and FTP
protocols. The photogrammetric adjustment and image processing
routines are written in JAVA. Different solutions are available for
the orientation of the digital stereopairs. The concept of running
photogrammetric software on the Internet is extended by a new
approach of architectural photogrammetry 3D modelling. The architectural
survey is monitored by underlying geometrical models stemming
from architectural knowledge. Image correlation, geometrical
functions and photogrammetry data are combined to optimize the modelling
process. The data of the stereoplotting are directly superimposed
on the images and exported towards CAD software packages
and VRML file format. ARPENTEUR is usable via the Internet at
[http://www.arpenteur.net].
4.1.5 3D object structures
Architectural photogrammetry 325
4.1.5.1 General remarks
If a person is asked to describe an object, he/she solves the problem typically
by describing all the single components of the object with all their
attributes and properties and the relations they have with respect to each
other and to the object. In principle computer representations and models
are nothing other than the analogue description of the object, only the
human language is replaced by mathematical methods. All kinds of representations
describe only a restricted amount of attributes and each finite
mathematical description of an object is incomplete.
Data models are necessary in order to process and manipulate real-world
objects with the computer. The data models are abstractions of realworld
objects or phenomena. Abstractions are used in order to grasp or
manipulate the complex and extensive reality. Each attempt to represent
reality is already an abstraction. The only complete representation of a
real-world object is the object itself. Models are structures, which combine
abstractions and operands into a unit useful for analysis and manipulation.
Using models the behaviour, appearance and various functions of an
object or building can be easily represented and manipulated. Prerequisite
for the origin of a model is the existence of an abstraction. Each model
needs to fulfil a number of conventions to work with it effectively. The
higher the degree of abstraction the more conventions have to be fulfilled.
CAAD models represent in an ideal way the building in form, behaviour
and function as a logical and manipulable organism.

326 Pierre Grussenmeyer et al.
The data of the computer internal representation, which is sorted according
to a specific order (‘data structure’), forms the basis for software
applications. The data basis is not directly accessed, but via available model
algorithms, which allow the performance of complex functions by transforming
them into simple basic functions according to a defined algorithm.
The representation of a real-world object in a computer-oriented model is
a synthesis of data structure and algorithms. Depending on extent and
amount of information of the data, an object can be represented as a dataintensive
or an algorithm-intensive model (Grätz, 1989). The most important
role in the definition of models plays a proper balance between correctness
and easy handling.
4.1.5.2 Classification of 3D models
In principle 3D models can be subdivided into three independent classes, the
wireframe model, the surface model and the solid model (see Figure 4.1.15).
The division is based on the different computer internal representation
schemes and is therefore also for the application areas of these models.
Wireframe models are defined by the vertices and the edges connecting
these vertices. They fix the outlines of an object and allow a view through
from any point of view. This is an advantage for simple objects, but reduces
the readability of more complex objects. This representation is therefore
often used for simple objects.
Surface models represent the object as an ordered set of surfaces in threedimensional
space. Surface models are mainly used for the generation of
models, whose surfaces consist of analytical not easily describable faces
having different curvatures in different directions. This is often the case
for models of automobiles, ships or aeroplanes.
Volumetric models represent three-dimensional objects by volumes. The
data structure allows the use of Boolean operations as well as the calculation
of volume, centre of gravity and surface area (Mäntylä, 1988).
Surface modelling is the most demanding but also the most calculationintensive
way of modelling. Solid models always represent the hierarchy
of the object, in which the primitives and operations are defined.
3D model
wireframe model surface model volume model
Figure 4.1.15 Overview of 3D models.

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Architectural photogrammetry 327
Each of the classes mentioned above has its specific advantages and
disadvantages. Depending on the task the advantages and disadvantages
are more or less important. Therefore it is not possible to make a general
statement, which of the classes is the best representation of a real-world
object.
Every representation of an object is a more or less exact approximation
of the reality. A true-reality representation of a building considers all important
attributes of the design. Looking at the section of a box object (see
Figure 4.1.16) shows the differences of the different representations.
• The wireframe model represents the box as a quantity of vertices and
edges. The section shows a quantity of non-connected points. This
representation is reality-true if one is interested in the general form or
in the position of the box.
• The surface model describes the box as a combination of vertices,
edges and surfaces. The section shows a quantity of points and lines.
This representation is reality-true if one is interested in the appearance
of the surfaces.
• The volumetric model shows the box as a quantity of vertices, edges,
faces and volume elements. The section shows points, lines and faces.
This representation is reality-true if one is interested in mass properties,
dynamic properties or material properties. For this purpose
additional information that does not belong to the pure geometry of
the object has to be evaluated.
Figure 4.1.16 Reality-true representation of a box as wireframe, surface and
volumetric model.

328 Pierre Grussenmeyer et al.
Figure 4.1.17 Example for ambiguity of a wireframe representation.
4.1.5.3 Wireframe models
The simplest forms of three-dimensional models are wireframe models. The
computer internal model is confined basically on the edges of the object.
Between those edges exists no relation, a relation to faces is not defined.
Information about the inside and the outside of the object is not available.
Points and edges are the only geometric elements of a wireframe model and
are represented in the computer by list structures.
If a quantity of edges is stored with the condition that these edges should
form the edges of a real-world object, it is often not unequivocal which
object is represented. There exists more than one object that have the same
edges as elements (see Figure 4.1.17).
The wireframe model allows therefore only an incomplete and ambiguous
representation of a real-world object, which requires human interpretation.
Manipulations are only possible on the basis of object edges (not
object oriented) with the result that, as a result of geometric operations,
nonsensical objects can be modelled. For example, deleting an edge of a
cube results in a wireframe model which has no representation in the real
world.
4.1.5.4 Surface models
The main information of the data structure of surface models is carried
in the single surfaces of the model. These surfaces are typically not easy
to describe by analytical means. A vector representation is also not possible.
As a mathematical representation of such surfaces, approximate procedures

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Z
Y
X
Architectural photogrammetry 329
v u
x = x (u, v)
y = y (u, v)
z = z (u, v)
Figure 4.1.18 Parametric representation of a surface (adapted from Grätz, 1989).
are often used, where the surface is represented between given points by
a parametric function. The three-dimensional coordinates of the surface
are a function of surface coordinates, which are used to parameterize the
surface (see Figure 4.1.18).
Quite a number of mathematical procedures to handle surface models
are available, such as Bézier approximations, spline and B-spline interpolations.
The surfaces in this data structure are quasi-independent elements, which
means that they have no relations to each other. Surfaces do not share
edges, the edges belong to the geometric description of the surfaces. A
relation between a surface and a volume does not exist. Therefore models
can be constructed, which are composed of a number of surfaces, but have
no representation in the real world.
4.1.5.5 Volume models
The third class of 3D models are the volume models, which covers quite
a number of different classes, such as parametric representation, sweep
representation, octrees, cell decomposition, boundary representations,
constructive solid geometry and hybrid models.

330 Pierre Grussenmeyer et al.
Characteristic for volume models is the computer internal volumetric
representation of three-dimensional physical objects of the real word. These
models are complete and non-ambiguous. Complete in this respect means
that it is impossible to define or represent a volume with a missing surface
or edge. On the other hand it is impossible to introduce surfaces or edges
into the model, which do not belong to a volume. The produced computer
model is in a technical sense a real representation of the reality. Therefore
nonsense objects, like in wireframe and surface models, are impossible.
Amongst the most commonly used volume models are the boundary
representation (BRep) and the constructive solid geometry (CSG).
The boundary representation (BRep) describes a three-dimensional object
by its boundary elements (faces, edges and vertices). A boundary representation
holds implicit a hierarchy in its data structure. An object is
defined by its faces, the faces by its edges, the edges by its vertices and
the vertices by three coordinates. A BRep model is organized in a topologic
part and in a geometric part. Whereas the topologic part describes
the neighbourhood relations between vertices, edges and faces, the
geometric part holds the geometric information about the topologic
elements (e.g. the three coordinates of the vertices). For the topologic relations
have to obtain the following rules:
• each object is in relation to a number of faces, which bound it;
• each face is in relation to a number of edges, which bound it;
• each edge separates two faces from each other;
• each edge is in relation to a number of vertices, which limits it.
The topologic description of the object describes it as an arbitrary
deformable object, which solidifies according to the geometric description.
Constructive solid geometry (CSG) describes the object instead of its
bounding faces and edges by a set of defined volumetric primitives and
basic operations of these primitives. The basic idea is that complex objects
are represented as ordered additions, subtractions and intersections of
simple objects. The primitives, which are used to sequentially build up the
model, are directly visible in the data structure. Hence, basic volumes like
cuboids, cones, globes, cylinders, etc. are contained in the data structure
as primitives and directly accessible. They form the lowest level of geometric
elements. An object is defined by the following grammar:
:: |
argument |
:: cube | cuboid | cylinder | cone | globe | . . .
:: translation | rotation | scaling
:: | | .

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Architectural photogrammetry 331
According to this grammar, each object is describable as a binary tree,
where the leaves represent the primitives and the nodes represent the operations
and transformations. The first node represents the modelled object.
With this scheme the hierarchy of an object is implicitly given.
Figure 4.1.19 gives an example of the different data structures of boundary
representation and constructive solid geometry of one and the same
object.
4.1.5.6 Hybrid models
Beside the ‘pure’ representations of object models often hybrid models are
utilized. Hereby the term ‘hybrid model’ is not clearly defined and is used
for various types of models, which use different representations within one
system. In principle the term can be used for all non-homogeneous models.
It is often used for systems that can handle wireframe and surface
models at the same time. Others use the term ‘hybrid model’ for using
volume and surface models under the same graphical user interface. Or
hybrid models are volume models, which use partly a CSG as well as a
Figure 4.1.19 BRep and CSG data structure of the same object.

332 Pierre Grussenmeyer et al.
BRep data structure in order to have a dual representation of generative
and accumulative elements. Hybrid models distinguish a primary structure,
which is responsible for the exact model and all relevant model
algorithms, and a secondary structure for specific tasks. The main task of
this secondary structure is often the fast visualization of objects on the
graphical screen.
4.1.6 Visual reality
Due to the progress in computer hard- and software there is a rapid development
in the facilities of visualization in architectural photogrammetry.
Simple facade plans are no longer suitable for the demands and applications
of many users. 3D-real-time applications such as animations, interactive
fly-overs and walk-arounds, which had needed the performance of
high-end workstations a few years ago, are now also available on personal
computers.
Two different concepts have to be distinguished. Where ‘Virtual Reality’
mainly uses vector models to describe a non-existing ( virtual) situation
or fiction, ‘Visual Reality’ means a complex combination of vectors,
surfaces and photo textures to visualize an existing object (‘photomodel’).
A fascinating idea is to merge these models into one, showing virtual
objects within a visualized reality.
Figure 4.1.20 Perspective view of 3D photomodel ‘Ottoburg, Innsbruck’.

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Architectural photogrammetry 333
Figure 4.1.21 Orthoimages in scale of 3 facades of photomodel ‘Ottoburg,
Innsbruck’.
According to the purpose and required accuracy of the result there are
numerous ways to create such textured 3D models. They range from
sticking ortho-rectified photos to geometrically simplified surfaces of
facades to a sophisticated reprojection of the original photos on to the
complex geometry of a building using interior and exterior orientation of
the camera.
Regarding these models of a monument’s 3D data as a basic storage
concept, a large number of resulting products can be derived from it. As
examples arbitrary perspective views and orthoimages in scale should be
referenced here.
A very promising way to visualize 3D-data is to create so-called ‘worlds’,
not only for computer games but also for ‘more serious’ applications. VRML
is a new standardized format (ISO 1997) describing three-dimensional
models and scenes including static and dynamic multi-media elements. This
description format is independent of the kind of computer. Most Internet
browsers support VRML file format. 3D object models can be viewed and
inspected interactively by the user or animated in real-time even on a PC.
Thus, VRML is well suited to create, for example, interactive environments,
virtual museums, visualizations and simulation based on real-world data.
Another way to visualize real-world objects is creating panoramic images.
This approach avoids the time-consuming process needed for a 3D model.
Plug-ins for Web browsers provide interactive movement. There are several
methods to achieve panoramic images. One is to take single images with
20 per cent to 50 per cent overlap from a fixed position while rotating
the camera around a vertical axis. Warping them on to a cylindrical or
spherical surface leads to a spatial imagination when navigating through
the model. Another way is to move the camera around the object with a
fixed target point. Complex objects can be so viewed and turned around
on a personal computer by simply dragging the mouse.

334 Pierre Grussenmeyer et al.
A combination of multiple panoramas or linking additional information
about the shown objects can be done using clickable ‘hot spots’. Special
panoramic cameras and authoring tools for image stitching are available.
The new image-based rendering techniques using synthesis of images
(among others to create panoramic views) also work without explicit 3D
models of the object. Parallaxes between two images suffice for interpolation
(sometimes even extrapolation) of others. They are restricted to
existing objects and cannot be to combined with virtual worlds.
4.1.7 International Committee for Architectural
Photogrammetry (CIPA)
To conclude this chapter in which an overview of recent developments
and applications in architectural photogrammetry are given, we briefly
present the International Committee for Architectural Photogrammetry
(CIPA), as a forum on this field.
CIPA is one of the international committees of ICOMOS (International
Council on Monuments and Sites) and it was established in collaboration
with ISPRS (International Society of Photogrammetry and Remote Sensing).
Its main purpose is the improvement of all methods for the surveying of
cultural monuments and sites, specially by synergy effects gained by the
combination of methods under special consideration of photogrammetry
with all its aspects, as an important contribution to the recording and perceptual
monitoring of cultural heritage, to the preservation and restoration
of any valuable architectural or other cultural monument, object or site, as
a support to architectural, archaeological and other art-historical research.
ISPRS and ICOMOS created CIPA because they both believe that a
monument can be restored and protected only when it has been fully
measured and documented and when its development has been documented
again and again, i.e. monitored, also with respect to its environment, and
stored in proper heritage information and management systems.
In order to accomplish this mission, CIPA [see http://www.cipa.uibk.
ac.at] will:
• establish links between architects, historians, archaeologists, conservationists,
inventory experts and specialists in photogrammetry and
remote sensing, spatial information systems, CAAD, computer graphics
and other related fields;
• organize and encourage the dissemination and exchange of ideas,
knowledge, experience and the results of research and development
(CIPA Expert Groups and CIPA Mailing List);
• establish contacts with and between the relevant institutions and
companies which specialize in the execution of photogrammetric
surveys or in the manufacture of appropriate systems and instruments
(Board of Sustaining Members);

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• initiate and organize conferences, symposia, specialized colloquia,
workshops, tutorials, practical sessions and specialized courses (CIPA
Events);
• initiate and coordinate applied research and development activities
(CIPA Working Groups);
• undertake the role of scientific and technical expert for specific projects
(CIPA Expert Advisory Board);
• organize a network of National and Committee Delegates;
• submit an annual report on its activities to the ICOMOS Bureau
(Secretary General) and the ISPRS Council (Secretary General) and
publish it on the Internet (Annual Reports);
• publish also its Structure, its Statutes and Guidelines on the Internet.
CIPA has a well-established structure of Working Groups (WG) and
Task Groups (TG):
• WG 1 – Recording, Documentation and Information Management
Principles and Practices;
• WG 2 – Cultural Heritage Information Systems;
• WG 3 – Simple Methods for Architectural Photogrammetry;
• WG 4 – Digital Image Processing;
• WG 5 – Archaeology and Photogrammetry;
• WG 6 – Surveying Methods for Heritage Recorders;
• WG 7 – Photography;
• WG 8 – Cultural Landscapes;
• TG 1 – Non-professional Heritage Recorders;
• TG 2 – Single Images in Conservation.
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Architectural photogrammetry 335
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Batic J., et al., 1996. Photogrammetry as a Method of Documenting the Cultural
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Dallas, R.W.A., 1996. Architectural and archaeological photogrammetry. In K.B.
Atkinson (ed.) Close Range Photogrammetry and Machine Vision. Whittles Publishing,
Caithness, UK, pp. 283–302.
Fondelli, M., 1992. Trattato di fotogrammetria urbana e architettonica (in Italian).
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Bryan, P.G., Corner, I., Stevens, D., 1999. Digital rectification techniques for architectural
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340 Michel Kasser
4.2 PHOTOGRAMMETRIC METROLOGY
Michel Kasser
4.2.1 Introduction
The term ‘photogrammetric metrology’ covers the whole range of metrology
activities that exploit photogrammetric processes, that is to say,
geometric processes based on image acquisition, and the image processing
which historically hardly ever took place in real time. The appearance of
digital imagery has been the origin of a significant change in this technical
domain, especially because it allowed real-time measures to be reached,
which opened many new markets. And then the use of CCD cameras also
permitted images of very large dynamics to be obtained, allowing the difficult
cases formed by uniform surfaces, very current in industrial metrology,
to be processed in a much better way. The very large dynamics makes it
possible to detect very weak differences of radiometry having a meaningful
character, which means they can be processed by automatic correlation.
Let us recall that photogrammetry is fundamentally a method founded
on angle measures, angles that are recorded permanently on the film or
in the digital pixel geometry. From this point of view it is easy to make
the link with metrology methods based on theodolites measures, which
are also used to measure angles, but with quite different devices. Therefore
there is a continuity of methodologies between these two domains, and
now that theodolites are digital, sometimes motorized, or capable of
pointing their targets automatically, one notes without surprise that the
same softwares are often used to process measures coming from these two
techniques.
There is also a continuity between photogrammetry and studies in
robotics to permit a fast identification of the geometric environment of
the robot. The robotics developed some continual measures based on video
images, allowing some elements in an image to be treated, this being
performed at very high speed in order to allow the calculator to choose
movements that the different motors have to perform. It is still photogrammetry,
but a very specialized one, and that one sometimes calls
videogrammetry.
Photogrammetric metrology finally represents all the methods using the
equation of collinearity (see §1.1) on images, but in conditions that differ
from the simple field of cartography. It represents a reuse of the body of
knowledge of photogrammetry, but for applications that are each different,
and that are rather specialized towards measures without contact with a
large amounts of points. Objects processed are generally of restricted sizes,
from about ten metres (wing of plane, cockles of boat) down to the
millimetre, or even less (inspection of tapped holes, of soldering, of surfaces
of samples checked with a microscope, etc.).

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4.2.2 Equipment
Photogrammetric metrology 341
The basis of modern digital photogrammetric metrology is the CCD
camera. This type of sensor has been used with all available matrix sizes,
from small-size matrixes for real-time applications up to 4k × 4k matrixes,
and probably more sooner or later. This matrix is set up as usual in the
focal plane of the optics, and as it is about doing measures these optics
must have some steady geometric parameters in the time, so that they can
make the object of a calibration. In this sense one doesn’t search now, as
in aerial imagery (see Chapter 2), for optics without distortion, but rather
for optics having an excellent resolution, and whose distortion is steady
in time, and the same for the position of their optic centre and their principal
planes.
This general type (CCD optics) can be used in very different ways. It
can first of all be used locally, like a traditional camera, with successive
positions of the same device or several synchronized devices, and while
identifying the points in images on which are done the external geometric
measures. The setting up of images is then achieved using traditional tools
of photogrammetry, with possible adaptations for geometries very different
from the aerial images with an almost vertical axis (e.g. problems of
refraction).
It can also be used fixed very rigidly to the optic axis of a theodolite,
which permits one to know the orientation in the reference frame corresponding
to every image with the considerable precision of the system
of angles measures of the theodolite. This whole is named phototheodolite;
it was used a long time ago with film or even glass plates cameras, but
has since fallen into obsolescence. If the theodolite is itself localized and
oriented, which is a simple operation, one gets images that possess all
parameters of localization and orientation, permitting an immediate setting
up to do directly photogrammetric restitution. One can also use only the
capacity of orientation of the theodolite to combine one set of images
obtained in the different directions (motorized phototheodolite), and to
get thus in a unique conical geometry an image having a very important
number of pixels.
One can also try to measure rapidly a large number of targets (for only
a few, a motorized theodolite with automatic aiming would be preferable),
while going very quickly, typically in some milliseconds. In this case one
uses retroreflecting targets, formed from many small plastic cubes’ corners
for example, and the optics used is then also equipped with an annularshaped
flash, which forms a circle completely surrounding the frontal lens.
Thus targets send back a considerable light quantity towards the objective,
and in return with a suitable threshold of the image one will see on
this one only luminous points on a black scene, every point corresponding
to a target. It will remain to identify these different targets on every acquired
image, which requires an approximate knowledge of the measured object.

342 Michel Kasser
4.2.3 Cases of use
The specificities of photogrammetric metrology must be looked for in relation
to other methods of measure, in order to identify its typical uses. We
may consider it especially useful in the following domains:
• when the measure must be acquired in a very short time on numerous
to very numerous points (from tens to hundreds of thousands of
points);
• when measures are to be performed without possible or desirable
contact (very hot objects, contaminated objects, objects for which no
pose of targets is admissible);
• when measures can be exploited only a long time after the acquisition
of the images: the image acquisition is an inexpensive part of the
complete photogrammetric operation, and image processes can be put
back to a later period, for example to measure the ageing of a given
object.
We will examine here some examples concerning one or several of these
domains.
Medical domain
Two situations are typical of this domain: the follow-up geometric of a
portion of the human body (lesions, tumours, dermatological problems,
but also identification of people by morphometric measures . . .), and the
surgical intervention from afar allowing a specialist to intervene quickly
on distant sites without displacing the patient or the surgeon. The second
one is again in development, but it is likely that it will be limited to
transmitting some stereoscopic images from a site equipped for a telemanipulation
of surgical instruments, and that photogrammetric aspects
will be quite reduced (possible 3D measures from afar). The first requires
more classic concepts. Being about a living surface, it will be necessary to
proceed to an instantaneous measure of two images forming a stereoscopic
couple. And as it is not simple to put in the field of every image some
elements permitting a formation of the model in differed time, the most
logical answer is to use two cameras fixed very rigidly in relation to each
other. Thus, once calibration measures have been achieved, one is able to
measure in 3D the part of the body appearing in the zone covered in stereoscopy.
An aid by automatic correlation gives assistance in pointing for
non-photogrammetres practitioners. However, as we will show in §4.2.4,
the extremely low variable radiometry of human skin requires a special
lighting so that the whole functions correctly.

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Photogrammetric metrology 343
Objects in movement
This is quite a tyical case for the use of photogrammetry. We are in the
presence of an object that distorts itself quickly, or of an object in movement,
and the number of points to measure is superior to a few units (if
the number is very low it can be performed with motorized automatic
pointing theodolites). Examples of such situations are numerous: study of
pieces distorting themselves under strain (tests of plane wings), dynamic
phenomenon studies (survey of the wave formation to the stem of a ship,
fall of blocks in an unsteady slope), etc. The images are in this case
necessarily acquired with several cameras, which must be synchronized
rigorously. The geometric elements allowing the setting up to be achieved
are obtained according to what is feasible, every situation forming a special
case: some known coordinate targets are in the field of cameras, or again
localization and orientation in the space of cameras are obtained by external
means (GPS, inertial systems, goniometric orientation . . .).
Controls of coppercraft pieces
Pieces of thick coppercraft cause subtle metrological problems: it is generally
about the control of the obtained shape in compliance with the initial
specifications. Some pieces of very large size can require that the reality
be very close to the surfaces calculated (propellers of ships, wings of
plane, parabolic reflectors for radio waves for telecommunications, radioastronomy,
etc.). The most economic solution here is still photogrammetry,
which permits the requested precision to be reached (often better than
1 mm) in a much more cost-effective way than other methods. The other
main technical solution consists in using some tridimensional measuring
machines, but these machines are limited in accessible measurements (the
largest ones don’t permit one to make measurements of objects larger than
3 m), and are slow (several seconds between every measured point), but
are on the other hand much more precise (they measure with a precision
of the order of the m). Besides, they are extremely costly, and pieces
must be brought to the machine, and not the reverse. Photogrammetry,
although not so precise, does not present these limitations. Besides, the
acquisition of the whole image can take place in a very short time, as we
already saw. Without reaching the complete simultaneity, which requires
arranging numerous cameras, it is possible to acquire the whole image if
need be in less than one hour. This type of possibility is profitable in the
case of large-sized objects for which the temperature creates distortions,
that cannot be controlled (objects installed outside, as for parabolic
antennas, ship sections intended to be fixed together, etc.).

344 Michel Kasser
Surveys of painted underground caves
We are here in the case of artistic productions, onto which it is sometimes
completely impossible to put targets considering the fragility of the object.
Photogrammetry permits measures without contact, without any risk of
destruction for the studied object. In counterpart, one sometimes expects
in such cases the possibility of restoring the acquired images under a plane
shape, or developed on a mean plane, which is evidently not possible
without the calculation of a complete 3D model of this object. So a fresco
achieved on a surface that includes numerous mouldings, or tracings of
animals on prehistoric underground caves, are cases in which elements of
reliefs of the cave walls may be an integral part of the tracing and are
therefore indispensable for the archaeologists’ interpretation. In such situations,
it is necessary to try to identify some precise and punctual details
in sufficient quantities that will be determined by classic topometric
methods. If this is not possible, one can create some relatively precise
temporary details while using low-power visible laser beams (red laser
diode pointers, or impacts of reflectorless laser EDMs, of Disto type (Leica)
for example). There is also the possibility of working with phototheodolites,
which can be used in order to deliver oriented and localized images
with a high precision. It allows images to be restored without using elements
of location in the images themselves. The inconvenience of this solution
resides in the impossibility of the operator guaranteeing himself against
a lawlessness of the material under utilization. For example, if the optic
axes of the theodolite and the camera have relative directions that
change without the knowledge of the operator (shocks, vibrations), it will
a posteriori induce mistakes that one will often not be able to correct.
It is then veritably a blind work.
Surveys of high-temperature objects
The possibility of measuring with absolutely no contact with the measured
object is therefore a classic field of the application of photogrammetry. So
to control streams of incandescent metal, there is virtually no equivalent
solution. Cameras are then adapted to such environments, but processes
done on images are always of photogrammetric type. One benefits then
from the capacity to measure without contact, as well as the one to acquire
images instantaneously. Two stationary, rigid cameras can be installed
permanently, and their relative positions will be the topics of a complete
calibration by taking images of a tridimensional object including targets,
whose relative positions will have been measured with a very high precision.

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Photogrammetric metrology 345
4.2.4 Typical problems of photogrammetric metrology
Photogrammetric metrology may be adapted, as a question of principle,
to situations that change often, and at each time it must be adjusted to
the different cases, as we have seen previously. Nevertheless, certain technical
problems are recurrent, because they are bound to the same bases
of the photogrammetric process. We will present here certain among them.
Case of uniform surfaces
This case is often encountered: a uniform surface will be defined here as
a surface whose apparent radiometry varies very little on an important
area. This very weak variation itself is a function of two parameters: the
dynamics of the sensor, and the real variation of the radiometry. The
reason why this dynamics is very important is it becomes possible to
measure some extremely reduced radiometry differences, and thus the
uniform zones become rarer and in any case of more reduced size than
with a more modest dynamics sensor. Surfaces of nearly uniform radiometry
are very frequent, and are met with in most of the previously evoked
cases. So in medical imagery, they are surfaces of skin, or in coppercraft,
surfaces of raw metal. On such surfaces it is then impossible to point with
the eye, and tools of automatic correlation may not be able to provide
some satisfactory indications. One solution may prove to be satisfactory
in such cases: it consists in using a special lighting if the situation permits
it. This lighting is chosen in order to project a whole set of random spots
on the object. For example, for a metric dimension object one will be able
to use a lighting provided by a retroprojector, on the tray of which
will have been arranged a film producing such very tight random spots.
Of course it will be necessary that the intended motive does not include
any periodicity, otherwise it will become very difficult to avoid false
correlations.
Case of reflecting surfaces
In the same way it will be impossible to process correctly by photogrammetry
reflecting surfaces without making a particular preparation of the
object to process. The solution proposed most frequently consists in such
cases (polite metal, glazing, etc.) of putting down a thin talc deposit, and
there again illuminating the surface while projecting some random spots.
The deposit of talc is easy to create, and doesn’t present any difficulties
being removed. But this method will not be capable of being put into operation
in some situations, and it is necessary to know how to anticipate
results then that will be locally mediocre (for example, liquid surface cases,
or again humid surfaces in decorated underground caves).

346 Michel Kasser
Numbering of targets
In most areas of photogrammetry, and it is of course the case in those of
metrology for which one searches for the best possible precision, one uses
targets of measurements adapted to the acquired images. These targets
serve to do the aerotriangulation on the one hand (even though the term
is not suited to cases of lack of aerial images, it remains used in spite of
everything) and the setting up of couples. On the other hand, targets may
be necessary as being points to be determined with the best precision: the
pointing on targets are indeed more precise than pointing on natural
surfaces. Some studies thus require a very large number of targets, and
the problem is that it is necessary to identify these targets, in order to be
able to find without error from one image to the other what are the homologous
points. When the object to survey is very large (architectural
photogrammetry, for example), the number of each target can be marked
by hand with chalk. But on objects of some metres, and especially if targets
are very numerous, this principle cannot be kept. One can then use labels
including bar codes, capable of being read automatically at the time of
the automated process of images. Nevertheless, this solution brings strong
strains on the orientation of these labels, as they can become illegible when
they are seen too much in perspective. When one uses classic reflecting
targets and an annular flash mentioned previously, it becomes possible to
localize targets automatically in the image by the use of a simple threshold.
In such a case, if one provides the software with the approximate geometry
of the object on which are the targets, it can itself then proceed to a
numbering of targets, which allows a considerable time to be saved at the
time of the exploitation of images.
4.2.5 Findings, perspectives
Photogrammetric metrology is a part of metrology that has still golden
days ahead. It permits some types of works to be processed in a much
more cost-effective way than any other methodologies. Besides, the appearance
of direct CCD digital images in the 1990s, opened the doors of the
real-time process. It must not be considered as a competitor with other
techniques (utilization of reflectorless EDMs, of laser scanners systems, of
tridimensional measuring machines). It is, for example, faster and more
precise that the first, slower, less exhaustive and much more precise that
the second, and for the third it is without contact, far less precise and
considerably faster. It can be adjusted to objects of all sizes, and one of
its essential steps (the image acquisitions) permits a storage that will allow
all the processes to be repeated if need be. It allows one not to process
images, therefore, and to keep them a very long time for possible future
processes. Finally, let us wager that this discipline will certainly progress
again, since it entered the digital era quite late. For example, one can

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Photogrammetric metrology 347
expect to see phototheodolites used more and more in metrology, to provide
measures of distortions of distant objects from afar.
The inter-techniques collaboration between photogrammetry, image
processing and robotics will probably provide many new tools in the next
few years.

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Index
adaptive filtering 93
adaptive sampling meshes 162
additive synthesis 27
aerotriangulation 6, 8, 12, 15, 62, 63,
78, 116, 118, 119, 120, 123, 124,
125, 126, 131, 132, 134, 135, 139,
140, 149, 156, 157, 287, 299,
346
airborne laser ranging systems (ALRS)
53, 54, 55, 56, 57, 58
ambiguities: matching 170, 207;
resolution of on flight 117
angular fields of view 34
atmospheric diffusion 16, 21, 22,
35
atmospheric refraction 1, 8, 12,
49
attenuation 17, 19, 20, 21, 22
basins 255, 268, 269
bundle restitution 304, 305
catchment areas 258, 264, 268, 270,
276, 277, 278, 281, 282
CCD 1, 14, 23, 24, 34, 36, 37, 38, 39,
41, 42, 43, 60, 61, 63, 66, 76, 153,
168, 288, 300, 307, 311, 312, 313,
314, 340, 341, 346
characteristic features 251
characteristic lines 164, 253, 255, 256,
257, 259, 271, 275, 277, 278, 294;
networks 280
CIPA (International Committee for
Architectural Photogrammetry)
300, 315, 334, 335, 336, 337, 338,
339
close range photogrammetry 337
collinearity 3, 13, 15, 124, 148, 155,
340; equation 3, 13, 124, 155
colorimetric spaces 26, 27, 32
compensation of forward motion 24
compression: algorithm 101, 105; by
fractals 114; of images 100; rates of
101, 104–6, 109, 114; reversible
101, 102, 103, 106; with losses 101,
104, 108
constructive solid geometry 330,
331
contour lines 159, 160, 164, 229, 230,
232, 233, 234, 239, 250, 256, 257,
266, 272, 277, 292
convolution operators 89
correlation templates 184
crests 234, 255, 256, 257, 258, 271,
278, 279, 280
cylindro-conical geometry 38
decorrelators 105, 108
Delaunay triangulation 162, 225, 229,
233, 235, 251
diffusion by sprays 17, 18
digital cameras 24, 41, 45, 56, 64, 67,
119, 124, 153, 158, 288, 294, 299,
311, 312, 314, 316
digital elevation models (DEM) 78,
159, 160, 168, 169, 181, 195, 197,
202, 208, 220, 224, 225, 226, 281,
282
digital photogrammetric workstations
(DPW) 59, 78, 145, 156, 176, 224,
300, 314, 323–4, 338
digital surface models (DSM) 43,
47, 49, 50, 53, 78, 159, 160,
162, 164–7, 194–6, 202, 210–25,
250, 288, 289, 301, 322, 323,
339
digital terrain models (DTM) 38, 46,
52, 55–8, 62, 78, 118, 131, 152,
156–60, 166, 168, 170, 177, 207,
212, 220–3, 229, 251, 255, 258,
261, 263–71, 277–87, 289, 294,
299, 314, 317

350 Index
digitization 39, 43, 58, 59, 60, 63,
64–5, 68, 76, 100, 152, 158, 164,
209, 253, 308, 310, 311; of aerial
pictures 58
discontinuities 29, 37, 61, 81, 162,
187, 190, 198, 200, 202, 211, 214,
216, 225, 254, 271, 280
disparity 125, 131, 137, 141, 177,
189, 192, 196, 200, 204, 205
distortion 1, 6, 12, 13, 14, 15, 23, 24,
37, 45, 63, 101, 104, 105, 108, 112,
114, 173, 176, 287, 302, 303, 319,
341
drainage networks 257, 258, 277,
281
dynamic programming 200, 202, 203,
205, 207
dynamics 43, 44, 46, 56, 57, 65,
76, 79, 81, 82, 85, 153, 340,
345
Earth curvature 7
elastic grid surfaces 231, 243, 246
entropy 103, 104, 105
epipolar lines 151, 174, 175, 180, 200,
202, 203, 205
epipolar resampling 148, 150, 152,
175, 176
equalization of histograms 82
false matches 188, 190, 216
field curvature 23
filtering 88, 89, 91, 93, 95, 99, 100,
111, 112, 131, 132, 141, 143, 156,
190, 217, 218, 219, 221, 224, 271,
279
fog 16, 17, 22, 23, 41, 44, 46
forward motion compensation (FMC)
36, 43, 60
GALILEO 115, 124
Gaussian filters 91
geographic information systems (GIS)
59, 155, 156, 220, 278, 285
geoids 7
geometric dilution of precision (GDOP)
122
glass plates 12, 14, 15, 62, 341
global positioning system (GPS) 8, 36,
37, 38, 42, 53, 54, 55, 56, 78, 115,
116, 117, 118, 120, 121, 122, 123,
124, 156, 285, 287, 343
GLONASS (see GALILEO)
GNSS 115, 124
hidden parts 15, 45, 46, 57, 190, 208,
222
histograms of images 79; manipulations
of 81
homologous points 125, 128, 129,
131, 132, 134, 137, 139, 140, 141,
142, 143, 152, 170, 171, 173, 175,
178, 179, 185, 187, 198, 202, 205,
318, 322, 346
homomorphic filtering 88, 95
hot spots 34, 172, 289, 291, 334
HSV (hue, saturation, intensity value)
space 27, 28, 29, 30
Huffman code 106, 107
ICOMOS 334, 335, 339
image pyramids 150, 320
index map 78, 124, 140, 142, 143
inertial measurement units (IMU)
118
interferogram 49, 50
interferometry 47, 48, 49, 50, 52, 53,
120, 164, 165
join-up lines 289
JPEG 102, 106, 108, 109, 112, 114,
153
Karhunen-Loève transform (KLT)
113
kinematics 118
lasers 1, 53, 54, 58, 118, 120, 164,
224, 225, 228, 289, 344, 346
linear filtering 89, 91
median filters 93, 97
meshes 160, 166, 255, 260, 261, 262,
263, 264, 267, 272, 281
Mie diffusions 16, 17, 18
multi-image texture and radiometric
similarity (MITRAS) 214
multi-image texture similarity (MITS)
213, 214
multi-image similarity function 212
multiplicity 96, 131
navigation 36, 54, 56, 115, 116, 118
noise 1, 22, 43, 50, 61, 62, 64, 65, 66,
68, 70, 71, 73, 76, 87, 88, 89, 91,
93, 94, 96, 97, 98, 99, 100, 103,
112, 116, 123, 136, 157, 167, 170,
183, 189, 208, 209, 211, 221, 225,
266, 312

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official national reference frame 285
orthoimages 212, 217, 289, 303
orthophotography 41, 46, 56, 59, 62,
118, 158–9, 221, 222, 223, 282,
283, 284, 285, 286, 288, 290, 291,
292, 299
ortho-templates 184, 192, 197
OTF (on the fly) 117, 122
passages 29, 33, 98, 140, 255, 256,
259, 269, 271
perspective 2, 6, 13, 14, 42, 43, 115,
116, 117, 120, 121, 131, 136, 137,
148, 157, 184, 203, 282, 316, 317,
333, 346
perspective centres 115, 116, 121
Photo-CD system 311
photogrammetric filtering 131
planarity of emulsions 14
points of interest 125, 127
pressurized planes 12
radar 1, 47, 48, 49, 50, 51, 52, 53,
120, 148, 165
radarclinometry 47, 48, 50, 51
radargrammetry 47, 48, 49, 50
radiance 17, 21, 22, 25, 34
radiometric balancing 288, 290
radiometric quality 62, 63, 64, 66, 73,
76, 77, 289, 310
raised structures 159, 202, 220, 221,
222, 224, 294
raster grids (RG) 160, 161, 212
Rayleigh diffusion 17, 18, 20, 22
reference atmosphere 9
refraction angles 10
rotation matrix 2, 4, 5
scanners 1, 38, 58, 59, 60, 61, 63,
288, 310, 311, 314, 336, 346
segmentation 34, 73, 221, 222, 223,
224
semi-metric cameras 308, 309, 310
shape from shading 48, 50, 52, 164,
165
shutters 24, 36, 121
similarity measures 125, 127, 169,
207
spectral bands 25, 33, 34, 112
Index 351
spectral decorrelation 112
stereo matching from image space
(SMI) 173, 183, 184, 186, 189–90,
192, 195, 198, 202, 211, 220, 251,
319
stereo matching from object space
(SMO) 183, 189, 190, 192, 195,
197, 200
stereopreparation 118, 123, 287
subpixel displacement 149
subtractive synthesis 27
summits 2, 266, 281
surface models 159, 303, 305, 328,
329, 330, 331
systematism 15, 66, 123, 124, 127,
257
terrestrial photogrammetry 10, 11, 14,
137, 162, 300
thalwegs 234, 239, 253, 255, 257,
258, 259, 260, 264, 265, 266, 267,
269, 270, 272, 275, 277, 278, 281,
282
thin plate spline surfaces 231, 236,
239, 240, 243
tie points 119, 124, 125, 126, 127,
130, 131, 132, 134, 135, 136, 140,
144, 156, 196
time delay integration (TDI) 24, 60
topographic surfaces 166, 167, 229,
231, 232, 233, 235, 236, 239, 243,
254, 257, 258, 266, 281
trajectography 38, 42, 116, 118, 119,
122
triangular irregular networks (TIN)
160, 162–4, 168, 196, 225–6,
231–2, 235, 251
trichromatic vision 26
vignettage 23, 45
visibility 19, 20, 21, 73, 122, 198,
289
volumetric models 326
VRML 325, 333
watersheds 255, 257
wavelet transforms 105, 108, 110,
111, 112, 113
wireframe models 326, 327, 328